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{"description":"Probstein, R.F. And Kemp, N.H. J. Ae. Scs. 27, 1960. This paper considers the problem of calculating viscous aerodynamic characteristics of blunt bodies at hypersonic speeds and at sufficiently high altitudes where the appropriate mean free path becomes too large for the use of familiar boundary-layer theory but not so large that free molecule concepts apply. Results of an order-of-magnitude analysis are presented to define the regimes of rarefied gas flow and the limits of continuum theory. Based on theoretical and experimental evidence, the complete navier-stokes equations are used as a model, except /very close/ to the free molecule condition. This model may not necessarily give the shock wave structure in detail but satisfies overall conservation laws and should give a reasonably accurate picture of all mean aerodynamic quantities. In this /intermediate/ regime there are two fundamental classes of problems.. A /viscous layer/ class and a /merged layer/ class, the latter corresponding to a larger degree of rarefaction. For the viscous layer class there is a thin shock wave, but the shock layer region between the shock and the body is fully viscous, although the viscous stresses and conductive heat transfer are small at the shock wave boundary. Here, the use of the navier-stokes equations with outer boundary conditions given by the hugoniot relations is justified. For the merged layer class, the shock wave is no longer thin, and the navier-stokes equations can be used to give a solution which includes the shock structure and has free-stream conditions as outer boundary conditions. A simpler procedure is presented for /incipient merged/ conditions where the shock may no longer be considered an infinitesimally thin discontinuity but where it has not thickened sufficiently to entail the /fully merged layer/ analysis. In this case we approximate the shock by a discontinuity obeying conservation laws which include curvature effects, viscous stresses, and heat conduction. For a sphere and cylinder it is shown that the navier-stokes equations can be reduced to ordinary differential equations for both the viscous and merged layer class of problems. Solutions of these equations, when used in connection with hypersonic flow problems, are in general only valid in the stagnation region. To illustrate the viscous layer solutions, numerical calculations have been performed for a sphere and cylinder with the assumption of constant density in the shock layer, which is a useful approximation at hypersonic speeds. To illustrate the merged layer solution, calculations have been carried out for a sphere using the incipient merged layer approximation. Results are presented for detachment distance, surface shear, and heat-transfer rate in the stagnation region of a highly cooled sphere flying at hypersonic speed. With decreasing reynolds number, the shear and heat transfer are shown to increase above the extrapolated boundary-layer values in the viscous layer regime and then to begin falling in the incipient merged regime. As the reynolds number decreases in the incipient merged regime, the density in the shock layer increases, and the static and stagnation enthalpy behind the shock decrease. Calculations performed for an insulated sphere show that, with decreasing reynolds number in the incipient merged regime, the density in the shock layer decreases,. The total enthalpy behind the shock and at the stagnation point increase so that they are higher than the free-stream total enthalpy,. And The stagnation-point pressure behaves like the total enthalpy. For the highly cooled cylinder in the viscous layer regime, the same quantities are presented as for the sphere. The increase found in shear and heat transfer above extrapolated boundary-layer theory is small, in agreement with vorticity interaction theory. A discussion is given of the behavior of available experimental data for viscous flow quantities in the intermediate regime and the behavior predicted by the results of the present calculations. Qualitative agreement is indicated.","title":"Various aerodynamic characteristics in hypersonic rarefied gas flow.","url":"cran.html#doc329"},
{"description":"Holder, D.W., pearcey, H.H. And Gadd, G.E. A.R.C., C.P. 180, february 1954. The interaction between shock waves and boundary layers has important effects in many problems of high-speed flow. This paper has been written as a guide to the literature on the subject, and as a critical review of the present state of knowledge concerning both the underlying physical processes and the practical applications. It will be clear to the reader that, although substantial progress has been made, our knowledge is still far from complete and that more work both of a fundamental nature and on specific applications is needed before the problem is understood sufficiently well for design purposes. Part i of the paper describes experiments on comparatively simple types of flow designed to provide fundamental information and to assist in the development of the theory. These experiments show that the interaction depends mainly on the mach and reynolds numbers and on the strength of the shock wave. In particular, the interaction of a shock wave with a laminar boundary layer is shown to produce much larger effects than if the boundary layer is turbulent. For most cases where the effects of the interaction are large enough to have serious practical consequences it is found that the boundary layer separates from the surface, and the difference between the interaction with laminar and turbulent layers arises mainly because the laminar layer separates much more readily in an adverse pressure gradient. The details of the interaction downstream of the separation point thus depend critically on the behaviour of the separated layer, and on the conditions under which it reattaches to the surface. Many of the features found in the fundamental experiments appear also in practical applications and these are considered in parts ii and iii of the paper. Although the emphasis hero is on the performance of aerfoils and wings moving at high subsonic speeds, the importance of the interaction in other examples such as at supersonic trailing edges and in supersonic intakes is also discussed briefly. The differences between the interaction with laminar and turbulent boundary layers are often a source of serious discrepancy between model experiments and full-scale conditions. For small-scale models it is, therefore, frequently essential to make the boundary layer turbulent by artificial means. Some of the difficulties involved in doing this, and certain of the more promising methods are briefly discussed. It is shown that experiments on models with transition fixed can be used to explain a number of aerodynamic effects encountered in transonic flight, and connected with the occurrence of shock-induced separation of the turbulent boundary layers. For both two-dimensional aerofoils and straight and sweptback wings, turbulent separation occurs for shocks above a certain strength which applies for both model and full-scale conditions full-scale conditions,. Differences in magnitude would be expected if the pressure recovery along the separated layer between the shock and the trailing edge is affected by reynolds number, but little information is at present available on this point. Most of the repercussions of turbulent separation on the steady-motion characteristics of aerofoils and wings can be traced to the associated reduction in the pressure recovery over the roar of the surface. This is because the pressure at the trailing edge controls the inter-relation between the two surfaces /so long as the flow at the trailing edge remains subsonic/, and in particular the relative movements of the shock waves and the extents of the local regions of supersonic flow. Certain unsteady-flow characteristics such as buffeting and control surface separation. Some evidence is presented on the influence of section shape on the occurrence and effects of separation, but in this, as in many other respects, information relevant to turbulent boundary layers is scarce. Some notes on the further work which is required are given in part iv of the paper.","title":"Interaction between shock waves and boundary layers, with a note on the effects of the interaction of the performance of supersonic intakes.","url":"cran.html#doc798"},
{"url":"cran.html#doc1313","title":"On the flow in a reflected shock tunnel.","description":"Holder, D.W. And Schultz, D.L. Arc r + m 3265, august 1960. The performance of a shock tunnel operated by the reflected-shock technique is examined theoretically neglecting viscous effects and high-temperature real-gas effects. Particular attention is given to disturbances to the flow at the nozzle entry caused by waves reflected from the contact surface when the operating conditions depart from those for that the first disturbance reflected from the contact surface is weak enough to be tolerated only within a small range of primary-shock mach number, m /E.G., 5 7 m 6 3 if the pressure at entry to the nozzle is to remain constant to 10 per cent/. Within this range, running times much longer than those obtained in 'straight-through' shock tunnels are predicted, the limitation usually being imposed by the arrival of the expansion wave originating at the diaphragm. Outside this range of mach number, the uniform-flow duration between the arrival at the nozzle entry of the primary shock and the first disturbance reflected from the contact surface is shown to be approximately equal to the time between the arrival of the primary shock and the contact surface in a 'straight-through' shock tunnel. At first sight it appears, therefore, that the advantages of reflected-shock operation are confined to a very narrow range of shock mach number, unless a heated driver gas is used in order to vary the mach number for further analysis suggests, however, that subsequent disturbances in the multiple wave reflection process between the contact surface and the end of the tube are relatively weak over a useful range of shock mach number. Thus, if the flow after the arrival of the early reflected disturbances is used for test purposes, long running times seem possible in theory without severe restrictions to the shock mach number. Experiments have been made in a shock tube and a shock tunnel to provide data for comparisons with the results of the simple theory. If allowance is made for viscous effects on the motion of the contact surface, fair agreement is found for the disturbances reflected and transmitted by the contact surface, and for the arrival of the expansion wave reflection process increases when the shock mach number is raised substantially above the 'tailored' value, and a limit to the usable flow duration may result. A striking feature of the results is a fall of pressure at the end of the tube immediately after reflection of the primary shock. This is attributed to attenuation of the reflected shock resulting from its interaction with the boundary layer on the wall of the tube. Further research is required to check this explanation, and to investigate the effects of reynolds number and of the cross-sectional shape and size of the tube. The effects of the tail and reflected head of the expansion wave originating at the main diaphragm are discussed. It is shown that the arrival of the reflected head at the nozzle entry may impose a severe limitation to the duration of uniform conditions at low shock mach number, and that the arrival of the tail may limit the flow duration at high shock mach number. Unless means can be devised to suppress the expansion wave, it is demonstrated that it is desirable to have alternative diaphragm positions in a tube required to operate over a range of shock mach number. It is concluded that running times of order 10 milliseconds at a shock mach number of 4, falling to, perhaps, 1 millisecond at a shock mach number of 8 seem possible in a shock tunnel of reasonable size by using reflected-shock operation with unheated hydrogen driving air. Because of the simplifying assumptions of the theoretical investigations, and the deficiencies of the apparatus used for the experiments, the present investigation must, however, be regarded as preliminary in character. Further research is required to check and extend the findings, and topics particularly requiring investigation are listed in the paper."},
{"description":"Miele, A.A. Aiaa jnl. 1, 1963, 168. The problem of minimizing the drag of a slender, two- dimensional or axisymmetric body in hypersonic flow at zero angle of attack is considered under the assumption that the pressure coefficient law is newton's impact law as modified by busemann in order to include centripetal acceleration effects. After the condition that the pressure coefficient be nonnegative is accounted for and after arbitrary conditions are imposed on, in addition to the thickness and the length, the enclosed area and the moment of inertia of the contour in the two-dimensional case and the wetted area and the volume in the axisymmetric case, the minimal problem is formulated as a problem of the mayer type and solved by the combined use of the euler-lagrange equations, the transversality condition, the erdmann-weierstrass corner condition, and the properties of the switching function. Particular attention is devoted to the class of problems such that, among the four quantities being considered, two are prescribed while the remaining are free. For these problems, the extremal arc is composed of two subarcs.. One is characterized by a positive pressure coefficient and is called the regular shape,. The other is characterized by a zero pressure coefficient and is called the free layer. In this connection, the analysis shows the existence of two different types of solutions depending on whether the thickness is given or free. If the thickness is given, the expression for the regular shape is a power law, and the transition from the regular shape to the free layer occurs in the second half of the body. In the two- dimensional case, the exponent of the power law is 1 if the length is given if the enclosed area is given, and 3 if the moment of inertia of the contour is given,. The transition point from the power body to the free layer is located at 50 percent of the length if the length is given, at 66 percent if the enclosed area is given, and at the axisymmetric case, the exponent of the power law is if the length is given, 1 if the wetted area is given, and if the volume is given,. The transition point from the power body to the free layer is located at 60 percent of the length if the length is given, at 70 percent if the wetted area is given, and at 80 percent if the volume is given. On the other hand, for problems where the thickness is free, the equation governing the regular shape is not that of a power body, and the point of transition to the free layer is located in the first half of the body. In the two-dimensional case, the transition point is at 28 percent of the length if the length and the enclosed area are given, at 32 percent if the length and the moment of inertia of the contour are given, and at 45 percent if the enclosed area and the moment of inertia of the contour are given. In the axisymmetric case, the transition point is located at 35 percent of the length if the length and the wetted area are given, at 39 percent if the length and the volume are given, and at 46 percent if the wetted area and the volume are given. For all of the cases considered, analytical expressions are obtained for the optimum shapes, the thickness ratios, and the drag coefficients.","title":"A study of slender shapes of minimum drag using the newton-busemann pressure coefficient law.","url":"cran.html#doc1201"},
{"description":"Callaghan, E.E., howes, W.L. Coles, W.D. And Mull, R.H. Naca R.1338. Aircraft structures located in the near noise field of a jet engine are subjected to extremely high fluctuating pressures that may cause structural fatigue. Studies of such structures have been limited by lack of knowledge of the loadings involved. The acoustic near field produced by the exhaust of a stationary turbojet engine having a high pressure ratio was measured for a single operating condition without afterburning. The maximum over-all sound pressure without afterburning was found to be about 42 pounds per square foot along the jet boundary in the region immediately downstream of the jet-nozzle exit. With afterburning the maximum sound pressure was increased by 50 percent. The largest sound pressures without afterburning were obtained on a constant percentage band width basis in the frequency range from 350 to 700 cps. Additional tests were made at a few points to find the effect of jet velocity on near-field sound pressures and to determine the difference in value between sound-pressure levels at rigid surfaces and corresponding free-field values. Near the jet nozzle, over-all sound pressures were found to vary as a low power (approx. Unity) of the jet velocity. Over-all sound-pressure levels considerably greater than the corresponding free-field levels were recorded at the surface of a rigid plate placed along the jet boundary. The downstream locations of the maximum sound pressure at any given frequency along the jet-engine-exhaust boundary and the longitudinal turbulent-velocity maximum of the same frequency along a small cold-air jet at 1 nozzle-exit radius from the jet axis were found to be nearly the same when compared on a dimensionless basis. Also, the strouhal number of the corresponding spectra maximums was found to be nearly equal at similar distances downstream. In addition to the magnitude and frequency distribution of the acoustic pressures, it is necessary to know the cross correlation of the pressure over the surface area. Cross-correlation measurements with microphones were made for a range of jet velocities at locations along the jet and at a distance from the jet. Free-field correlations of the over-all sound pressure and of the sound pressure in frequency bands from 100 to 1000 cps were obtained both longitudinally and laterally. In addition, correlations were obtained with microphones mounted at the surface of a rigid plate that was large compared with the distance over which a positive correlation existed. The region of positive correlation was generally found to increase with distance downstream of the engine to 6.5 nozzle-exit diameters, but remained nearly constant thereafter. In general, little change in the correlation curves was found as a function of jet velocity or frequency-band width. The distance from unity correlation to the first zero correlation was greater for lateral than for longitudinal correlations for the same conditions and locations. The correlation curves obtained in free space and on the surface of the plate were generally similar. The results are interpreted in terms of pressure loads on surfaces.","title":"Near noise field of a jet engine exhaust.","url":"cran.html#doc721"},
{"description":"Experimental measurements of pressures and heat-transfer rates over three blunt afterbodies of small fineness ratio in fully separated wakes are presented. The afterbodies are generally similar in shape but have different stepdown heights from the end of the forebody. Tests were made by means of a new shroud technique over a range of reynolds numbers closely corresponding to typical flight conditions at mach numbers on the order of 20, considering models on the order of 5 ft. In diameter at about 120, 000 ft. Altitude. Stagnation temperatures on the order of 1, 300 R. To strictly speaking, the test flows correspond to prototype flows which would be created by a forebody consisting of a sharp or slightly blunted 54 half angle cone which turns cylindrical for a short distance and then connects with the afterbody. Judiciously interpreted, the results may be considered to have a somewhat wider applicability for approximation purposes. The results are presented and compared with each other in terms of nondimensional variables based on flow conditions at the end of the forebody. The pressure distribution along an afterbody is seen to be roughly uniform in each run. For a given point on an afterbody, the ratio of pressure to the stagnation pressure at the forebody end (or exit) decreases with increasing stagnation pressure or reynolds number. The present pressures and pressure-reynolds number variations (fig. 8) are compared with values obtained from chapman's mach 2 or 3 base-pressure data,. Qualitative and some quantitative agreement is noted. In the reynolds number range comparable to those of the present tests, chapman's exit boundary layers were considered to be laminar. An approximate check of the heat-transfer rate at the forebody end in the present tests also indicates a laminar rate. No information was obtained concerning the possible transition of the free-mixing separated boundary layer covering the wake. An adverse pressure gradient on the cylindrical end of the forebody figs. 7(a) and 7(c) was observed. Heat-transfer rates are seen to be roughly uniform over an afterbody in each run, although some increase in the streamwise direction is noted. The afterbody nusselt number (n) varies with the reynolds number (r evaluated at the forebody end) roughly in the manner n r where generally (fig. 13). Heat rates on the rear faces of the afterbodies are almost twice the values on the sides. The heat rates on the large-step body are higher than those on the body of zero stepdown height. In an addendum, it is shown that the prandtl-meyer expansion angle of the flow leaving the afterbody increases with increasing test reynolds number, and that the corresponding local mach number square increases linearly with reynolds number. The effect is to keep the local wake reynolds numbers virtually constant with increasing test reynolds number while the afterbody heat rates increase sharply. The expansion angle on the afterbody of zero stepdown height is significantly smaller than on the stepped down bodies,. This may affect the decreased heat rates on this body.","title":"On transverse vibrations of thin, shallow elastic shells.","url":"cran.html#doc1040"},
{"description":"Haines, A.B., holder, D.W. And Pearcey, H.H. Arc r + m3012, 1954. The major scale effects at high subsonic and transonic speeds arise from differences between the conditions under which laminar and turbulent boundary layers separate, and in how they behave after separation. For turbulent boundary layers, these conditions and behaviour do not vary greatly as the reynolds number is changed and in many examples, it has been shown that they are similar for the turbulent layers that occur naturally at high reynolds number and for boundary layers in which transition to turbulent flow is fixed artificially. The scale effects arising in wind-tunnel tests made at low reynolds number may, therefore, often be minimised by fixing transition to turbulent flow by introducing an artificial disturbance such as that produced by excrescences attached to the surface. The fact that the effects of separation are often less severe for laminar layers than for the turbulent layers that are likely to be encountered at full scale, makes it all the more important to do this whenever possible. Several methods which can be used to fix transition are described, and the results obtained by using them are compared. In general, in experiments in two-dimensional flow, good agreement is found, and explanations can be advanced for cases in which discrepancies occur. Several uncertainties and difficulties that arise in fixing transition are discussed and illustrated by examples. In particular, special care is needed in interpreting the results obtained with transition fixed at very low reynolds numbers (say, less than about r = 1 x 10 based on local chord for wings of about 0.1 thickness chord ratio and possibly higher reynolds numbers for thinner wings). The difficulties of fixing transition satisfactorily are increased for three-dimensional wings, particularly if they are swept-back or highly tapered (I.E., small chord and reynolds number near the tip) and if the tests cover a large range of incidence including high incidences for which the flow may separate from very close to the leading edge. Under these circumstances, it is frequently necessary to place the excrescences at different chordwise positions for low and high angles of incidence, and this is inconvenient in practice. More research is needed before sound recommendations can be made as to how and where transition should be fixed on such models, particularly since in routine testing, it is often not possible to check the effects of transition-fixing fully. In the sections dealing with three-dimensional tests, examples are given of the spurious results that have been avoided successfully by fixing transition, of the conditions where even at low reynolds numbers artificial fixing of transition may not be necessary to give a turbulent boundary layer ahead of the shock, and of the conditions under which there are some doubts whether the methods used for fixing transition have been satisfactory.","url":"cran.html#doc315","title":"Scale effects at high subsonic and transonic speeds and methods for fixing transition in model experiments."},
{"description":"Rodden, W. +. And Revell, J.D. J. Ae. Scs. 1960, 451. The shock tube is shown to be a feasible research tool for conducting boundary-layer transition experiments. The use of the shock tube permits the study of transition with highly cooled boundary layers, as may be encountered on hypersonic vehicles. Boundary-layer transition investigations have been made on optically polished pyrex hemisphere-cylinder and ellipse-cylinder models with stagnation-to-wall enthalpy ratios between 4.5 and roughness estimated to be less than 1 microinch (rms). Transition was detected by measurements of the heat-transfer rates on the model surface. The shock tube experiments indicated that a characteristic feature of transition of a highly cooled boundary layer on a hemisphere was the simultaneous occurrence of transition over the entire supersonic portion of the hemisphere. This implies that transition first occurred in the sonic region. The transition reynolds number (based on local fluid properties at the outer edge of the boundary layer and the momentum thickness) in the sonic region increased from about 225 to 325 as the stagnation- to-wall enthalpy ratio increased from about 9.5 to 29.5. Transition occurred along the cylindrical portion of the hemisphere-cylinder model at a nearly constant momentum thickness reynolds number, increasing from about 400 to 625 as the stagnation- to-wall enthalpy ratio increased from about 9.5 to 29.5. The highly cooled boundary layers obtained on the cylindrical portion of the shock tube hemisphere-cylinder model provided an extension of nasa transition results obtained on a cooled hemisphere-cone-cylinder model in a wind tunnel. The transition reynolds numbers obtained from these shock tube data were of the same order of magnitude as the minimum transition reynolds numbers obtained in the wind-tunnel experiments. The results indicate that, for practical purposes, boundary-layer cooling is not a critical transition parameter for blunt bodies with a highly cooled boundary layer resulting from a stagnation- to-wall enthalpy ratio of about 3 to 30. That is, the transition reynolds number did not vary significantly with boundary- layer cooling in this cooling range, but transition always occurred at a low reynolds number (between about 350, 000 and 750, 000 based on local external properties and a distance along the body surface from the stagnation point). The boundary-layer history (body shape history) appeared to be an important parameter affecting the magnitude of the reynolds number for transition and the amount of increase in the transition reynolds number with increased boundary-layer cooling. That is, transition occurred at a lower reynolds number on the ellipse-cylinder configuration than on the hemisphere-cylinder. Also, the increase in transition reynolds number with an increase in boundary-layer cooling was even less significant for the ellipse-cylinder than the hemisphere-cylinder.","title":"Oscillatory aerodynamic coefficients for a unified supersonic hypersonic strip theory.","url":"cran.html#doc272"},
{"description":"Lin, C.C. Pt.iii - stability in a viscous fluid. Q. App. Math. 3, 1945, 273. This is the last part of the author's theory of the stability of plane laminar motion. (for parts 1 and 2, cf. The same quart. 3, 117-142, 218-234 (1945),. These rev. 7, 225, 226.) the stability character of a viscous fluid is considered in detail. The author proceeds first to give a proof of a criterion of stability due to heisenberg.. If a velocity profile has an number and phase velocity, the disturbance with the same wave number is unstable in the real fluid when the reynolds number is sufficiently large. This destabilizing effect of viscosity is one of the most interesting phenomena in the general stability theory,. Its physical and mathematical significance is carefully discussed. The author then discusses the behavior of the so-called neutral curve for the two characteristic types of velocity distribution, the boundary layer type profile and the symmetrical profile. The asymptotic behavior of the neutral curve is discussed first. The main difference between profiles with and without a point of inflection is that the two branches of the neutral curve approach and for profiles with a flex, but both converge to for the profile without a flex. The most important results are as follows. For sufficiently large reynolds number R. (2) there always exists a minimum r below which the motion is stable. A similar result was obtained by synge from energy considerations. Synge found a limiting curve below which the motion is necessarily stable. The author's discussion of the asymptotic behavior of the curves shows further that there always exists a maximum value of a beyond which the motion is stable for all reynolds numbers. Hence the qualitative shape of the curve is determined. The author proceeds to show that simple approximate expressions for the stability limit can be obtained from his general analysis for a given velocity profile. These approximate stability limits for plane poiseuille flow and blasius flow are found to be r=5906 and r=502. The reynolds numbers are based on the width of the channel and the displacement thickness, respectively. Finally, the method for computing the complete instability curve is presented and the plane poiseuille case and the blasius problem worked out in detail. The stability limit for blasius flow had been given before by tollmien and schlichting. The present more exact computations agree well with tollmien's result as far as the minimum critical reynolds number is concerned. The value found here is r=420. The neutral curve for poiseuille motion had not been obtained before. The minimum critical number here is found to be r=5314. The agreement with the estimate from the simple criterion mentioned above is thus very good. A discussion of the physical significance of the viscous effects and of future developments concludes the paper.","url":"cran.html#doc417","title":"On the stability of two dimensional parallel flows."},
{"description":"Probstein, R.F. And Elliott, D. J. Ae.scs. 28, 1956, 206. The viscous transverse curvature effect in compressible axially symmetric laminar boundary-layer flow has been investigated, and it is found that the effect is characterized by the parameter which is essentially the ratio of the boundary-layer thickness to body radius. It is shown that the busemann and crocco integrals of the two-dimensional energy equation for are still valid for axially symmetric flow in which the transverse curvature effects are considered. By a generalization of mangler's transformation it is then shown that the boundary-layer equations are reducible to an almost two-dimensional form, making the analysis simpler for two asymptotic flow regions characterized by and less than or of the order of unity. It is with the latter region that the present paper is primarily concerned, and for this case it is shown that the additional term in the momentum and energy equations, which differentiates them from the two-dimensional form, behaves like an external favorable pressure gradient. Except for certain special cases it is necessary to obtain the of the order of unity by means of asymptotic expansions in ascending powers of a parameter that is small compared to unity but proportional to. It is shown how the asymptotic solutions can be found for (1) the velocity and temperature distributions for the compressible zero pressure gradient case when the body shapes are given by and and (2) the velocity distribution for incompressible flow with an external velocity of the form past a body given by. The zeroth approximation is the mangler result. For the cases of a linear external velocity distribution, similar profiles can be found for all values of. More generally it is shown that similar profiles exist if the exponents n and m satisfy the condition that. Here, similar is used in the restricted meaning that the distributions are derivable from ordinary differential equations. In the case of the cone and cylinder with zero pressure gradient where the equations have been numerically integrated for, the first-order correction to the mangler formulation shows that the effect on both the skin-friction coefficient and heat-transfer rate can become appreciable in the range where is less than or of the order of unity. At a constant, the effects are increased in magnitude when either the ratio of wall to free-stream temperature, or mach number, is increased. Also, all other conditions being equal, for the same value of the skin-friction coefficient and heat-transfer increase on the cylinder is greater than that on the cone. For flows with pressure gradient, the transverse curvature term behaves again like a favorable pressure gradient and tends to delay both separation and transition when compared with axially symmetric flows in which the transverse curvature effect is neglected.","title":"The transverse curvature effect in compressible axially symmetric laminar boundary layer flow.","url":"cran.html#doc94"},
{"title":"Viscous and inviscid stagnation flow in a dissociated hypervelocity free stream.","url":"cran.html#doc576","description":"Inger, G.R. Proc. 1962. Heat transfer and fluid mech. Inst. High reynolds number hypersonic stagnation flow over a blunt-nosed body in a nonequilibrium dissociated free stream is analyzed and compared to a similar flow in an initially undissociated ambient gas. Free stream dissociation effects on various equilibrium stagnation flow properties in air are presented as a function of the ambient atom mass fraction and dissociation energy for velocities ranging from 15, 000 to 25, 000 fps. Significant changes in the bow shock geometry, stagnation gas state, and boundary layer behavior are found when the free stream dissociation involves more than 10( of the total energy. It is observed that for large amounts of both atomic oxygen and nitrogen ahead of the body, the equilibrium shock layer properties converge toward those pertaining to chemically and vibrationally-frozen flow across the bow shock. Moreover, under certain conditions, the ionization level can be increased by an order of magnitude and the usual reduction in frozen boundary layer heat transfer due to a highly-cooled noncatalytic surface can increase from stall of adjacent stages. The effects of compromises of stage matching to favor part-speed operation were also considered. This phase of the study indicated that such compromises would severely reduce the complete-compressor-stall margin. Furthermore, the low-speed stage stall problem is transferred from the inlet stages to the middle stages, which are more susceptible to abrupt-stall characteristics. The analysis indicates that inlet stages having continuous performance characteristics at their stall points are desirable with respect to part-speed compressor performance. These characteristics must, however, be obtained when the stages are operating in the flow environment of the multistage compressor. Alleviation of part-speed operational problems may also be obtained by improvement in either stage flow range or stage loading margin. The results of this analysis are only qualitative. The trends obtained, however, are in agreement with those obtained from experimental studies of high-pressure-ratio multistage axial-flow compressors, and the results are valuable in developing an understanding of the off-design problem. In addition to these stage-matching studies, a general discussion of variable-geometry features such as air bleed and adjustable gas model. Numerical solutions of non-equilibrium airflows with fully coupled chemistry provide a preliminary verification of such scaling for benser, W.A. Limit characteristics. The analysis indicated that all these problems could be attributed to discontinuities in the performance characteristics of the front stages. Such discontinuities can be due to the type of stage stall or to a deterioration of stage performance resulting blades is included."},
{"url":"cran.html#doc244","title":"An improved smoke generator for use in the visualisation of airflow, particularly boundary layer flow at high reynolds numbers.","description":"Preston, J.H. And Sweeting, N.E. Arc r + m 2023, 1943. And Rapid method by which boundary layer flow was rendered visible has been previously described in the journal of the royal aeronautical society. It gave promise of being useful at the highest tunnel speeds provided a denser smoke could be obtained, which at the same time was free from the troublesome deposits associated with the wood smoke. Of the aerodynamics division attempts were made by the fuel research station to improve the density of the wood smoke and to reduce the deposits. These they showed were conflicting requirements, and whilst some improvement was effected, it was not sufficient for observation in the new tunnels at high speeds. The staff of the director-general of scientific research and development, ministry of supply, was then approached and it was decided to develop an oil smoke generator from a simple generator of this type which was demonstrated to us. This has been done successfully. The final apparatus in contrast to the wood smoke generator is light and compact. It takes only a few minutes to start and can be run as long as desired. Improvement on the wood smoke both as regards density and freedom from deposits, which cause premature transition. The density and quality of the smoke are now under control. Smokes ranging from a light smoke of bluish white colour to a heavy smoke dense white in appearance can be obtained. The oil smoke retains the advantages of the wood smoke in that it is non-corrosive and non-irritant, and the smell can be tolerated even when it is present in a considerable concentration. A certain amount of condensation is inevitable with oil smokes, but with suitable precautions troubles arising from this can be avoided. A dry solid smoke made by melting a hard wax was successfully generated with the same apparatus. Unfortunately because of its flocculent nature this smoke gave rise to solid deposits when passed through bore tubing, leading eventually to complete blockage. This seems to be a feature of solid smokes. The apparatus has been used to determine transition and laminar separation points on model wings in a number of the national physical laboratory tunnels. Smoke filaments have been maintained in the laminar state up to wind speeds of 180 ft. Sec. In the new tunnels. There is much to be said for making a standard practice of visualising boundary layer flow on models, particularly as the technique is simple and rapid. It would greatly assist the interpretation of force measurements and the more detailed explorations of the boundary layer by total head tubes and hot wires. The use of oil smoke is not limited to boundary layer flow visualisation. The apparatus described in this report would seem to be particularly suited for educational work in small demonstration tunnels."},
{"url":"cran.html#doc927","title":"Investigation of normal force distributions and wake vortex characteristics of bodies of revolution at supersonic speeds.","description":"Mello, J.F. J. Ae. Scs. 1959, 155. The supersonic aerodynamic characteristics of inclined bodies of revolution at high angles of attack have been investigated in order to provide a more basic understanding of the body vortex wake flow and its relation to the problem of body-wing interference. The results of wind-tunnel tests, whereby the normal force, pitching moment, normal force distributions, and the local flow properties in the vicinity of the body were determined, are discussed and analyzed. Comparisons of experimental normal force coefficient and center of pressure data with values calculated in accordance with theories which include methods for estimating the effects of viscosity show that the accuracy of these estimates is strongly dependent on the body fineness ratio and the angle of attack. Further comparisons of the distributions of theoretical and experimentally derived cross-flow drag coefficients clearly show that, in general, the disagreement between experiment and existing theories is due to the inadequate prediction of the magnitude and distribution of the forces resulting from flow separation. The circulation strengths of the concentrated vortices and the circulation strengths of the vortex feeding sheets in the body vortex wake are determined by closed-contour velocity-perimeter integrations for paths enclosing the vortex or the feeding sheet. The values of vortex strength calculated in this manner are in close agreement with the values predicted by vortex strength formulas written for a simple theoretical model for which it is assumed that the cross-flow in any plane along the cylindrical portion of the body is represented by the steady incompressible potential flow about a cylinder, two symmetrical vortices of equal strength, and the attendant image vortices. However, in computing these strengths it is necessary to use the vortex locations and the viscous normal force distributions determined from experiment. The experimentally determined values of vortex strength are, in turn, used to calculate--by means of the aforementioned incompressible cross-flow potential--the local flow inclination angles which are in good agreement with the measured values, except in the vortex core, in the vicinity of the feeding sheet, and in regions for which transonic cross-flow velocities are expected. A consideration of these various regions with simple methods which account for the observed phenomena leads to substantial improvement in the agreement between theory and experiment. It is indicated that the complete vortex wake flow may be adequately predicted for a body of revolution (for conditions represented by the theoretical flow model), provided that the distribution of the viscous normal force and the vortex locations are accurately known."},
{"title":"Some low speed problems of high speed aircraft.","url":"cran.html#doc792","description":"Spence, A. And Clean, D. J. Royal aero. Soc. V. 66, april 1962, pp 211-225. The first part of the paper deals with the low speed aerodynamics of aircraft shapes suggested by kuchemann, at the second international congress in aeronautical sciences at zurich in 1960, as suitable for achieving a required range at supersonic speeds, namely wingbody arrangements with sweepback angles of 55degrees or 60degrees and streamwise thickness-chord ratio of about 5 per cent suitable for low supersonic speed, and slender near-triangular wings with sharp leading edges suitable for mach numbers of about 2 or more. No attention is given to /slewed/ wings, powered lift or variable geometry. In dealing briefly with swept wings, the need for avoiding separation of flow from the leading edge is demonstrated, with the conclusion that it is desirable to use leading edge flaps with blowing or suction at the knee together with blown trailing edge flaps. Wind tunnel tests are described on a simplified model with these boundary layer control methods applied. Mention is made of the possibility of adverse ground effect on maximum lift. More attention is given to the case of slender wings because their use involves a new type of flow with separation from all edges. This flow and its steadiness are therefore discussed from the point of view of the possibility of buffeting,. The effect of plan form on static longitudinal stability and pitch-up is analysed,. And A short summary of available results on damping in pitch is given. Large rolling moments due to sideslip are shown to give rise to serious problems of control, and the present state of knowledge of static lateral and directional stability and rolling and yawing rotary derivatives is discussed. Finally the effects of proximity to the ground are summarised. The second part of the paper is concerned with work aimed at clarifying some of the requirements for handling qualities of future aircraft. It is not so much concerned with forecasts of the dynamic behaviour of these future aircraft as with determining what the pilot wants. Two aspects of control in the vertical plane are discussed in some detail namely speed control and glide path holding. Flight tests on an avro 707a aircraft, with artificially worsened characteristics, are described, and it is shown that substantially constant performance in the piloting task can be achieved at the expense of increased pilot effort. Some tentative conclusions on desirable levels of speed stability and phugoid damping are, nevertheless, drawn. A brief review of the present status of lateral/directional handling requirements, using mainly american data, is also included."},
{"description":"Jackson R. Stalder and david jukoff Report 944 A general method has been developed, using the methods of kinetic theory, whereby the surface temperatures of bodies can be calculated for steady flight at any speed in a rarefied gas. The particular solution was made for a flat plate., however, the calculations can be easily extended to bodies of arbitrary shape. It was found that the aerodynamic heating problem in the absence of solar radiation, that is, for the case of nocturnal flight, becomes of negligible importance at altitudes of 125 miles and higher and up to steady flight speeds of 36, 000 feet per second. The effect of solar radiation, for the case of daytime flight, becomes increasingly important as the flight altitude is increased. At an altitude of 150 miles and higher, solar radiation is the predominating factor that determines skin temperature. Owing to the strong effect of solar radiation on skin temperatures at high altitudes, the desirability of nocturnal flight is indicated in order to minimize skin temperatures. In order to maintain low skin temperatures, it was found that the angle of inclination of the body with respect to the flight path should be kept as small as possible. This may be accomplished in practice by designing the body to be finely tapered and by flying the body at small angles of attack. It is pointed out that skin temperatures may be reduced by insuring thermal contact between portions of the skin inclined at positive and negative angles with respect to the flight path. As much surface as possible should be inclined at negative angles. Practically, this may be accomplished by boattailing the body. In the event that an internal skin-cooling system is employed, it is shown that the rate of internal cooling must be of the same order of magnitude or greater than the rate at which heat is lost naturally by emitted radiation. If the cooling rate is below the natural radiation rate, cooling has little effect upon skin temperatures. It is shown that, in the case of a missile designed to fly over a wide range of altitudes and speeds, it is desirable to make the emissivity of the skin as high as possible. This conclusion, however, is based upon a skin surface for which the emissivity is independent of the wave length of the emitted and absorbed radiant energy. A possible method of reducing surface temperatures is indicated by the decrease in skin temperature which accompanies a decrease in thermal accommodation coefficient. This phenomenon may be used to advantage if it is possible to decrease the accommodation coefficient by altering the surface characteristics of the skin.","url":"cran.html#doc1147","title":"Heat transfer to bodies traveling at high speed in the upper atmosphere."},
{"url":"cran.html#doc928","title":"A new theory for the buckling of thin cylinders under axial compression and bending.","description":"Donnell, L.H. Asme trans. 56, 1934, 795. The results of experiments on axial loading of cylindrical shells (thin enough to buckle below the elastic limit and too short to buckle as euler columns) are not in good agreement with previous theories, which have been based on the assumptions of perfect initial shape and infinitesimal deflections. Experimental failure stresses range from 0.6 to 0.15 of the theoretical. The discrepancy is apparently considerably greater for brass and mild-steel specimens than for duralumin and increases with the radius- thickness ratio. There is an equally great discrepancy between observed and predicted shapes of buckling deflections. In this paper an approximate large-deflection theory is developed, which permits initial eccentricities or deviations from cylindrical shape to be considered. True instability is, of course, impossible under such conditions,. The stress distribution is no longer uniform, and it is assumed that final failure takes place when the maximum stress reaches the yield point. The effect of initial eccentricities and of large deflections is much greater than for the case of simple struts. Measurements of initial eccentricities in actual cylinders have not been made,. However, it is shown that most of these discrepancies can be explained if the initial deviations from cylindrical form are assumed to be resolved into a double harmonic series, and if certain reasonable assumptions are made as to the magnitudes of these components of the deviations. With these assumptions the failing stress is found to be a function of the yield point as well as of the modulus of elasticity and the radius-thickness ratio. On the basis of this a tentative design formula (5) is proposel, which involves relations suggested by the theory but is based on experimental data. It is shown that similar discrepancies between experiments and previous theories on the buckling of thin cylinders in pure bending can be reasonably explained on the same basis, and that the maximum bending stress can be taken as about 1.4 times the values given by equation buckling problems can probably be explained by similar considerations, and it is hoped that this discussion may help to open a new field in the study of buckling problems. The large-deflection theory developed in the paper should be useful in exploring this field, and may be used in other applications as well. The paper presents the results of about a hundred new tests of thin cylinders in axial compression and bending, which, together with numerous tests by lundquist, form the experimental evidence for the conclusions arrived at."},
{"title":"On the aerodynamic noise of a turbulent jet.","url":"cran.html#doc1244","description":"Cheng, sin-I. J. Ae. Scs. 1961, 321. A new model is advanced for analyzing the broad-spectrum noise of a turbulent jet. The shear layer bounding the turbulent jet is assumed to play an important role in modifying the / quadrupole sound radiation/ from the interior. To the sound- emitting small-scale turbulent eddies (with frequencies much higher than those of large-scale eddies), the laminar shear layer has an irregular contour, as if the large-scale turbulent motions were frozen. The linearized analysis is then applied to the laminar shear layer to relate the acoustic oscillations across it. The concept of geometrical acoustics is generalized to represent the passage of an acoustic ray through a laminar shear layer. Acoustic rays may be traced across the shear layer as transmission and refraction, but they may also be apparently /absorbed/ or /generated/ by the laminar layer. This /generation/ is visualized as the schematic representation, within the framework of geometrical acoustics, of the action of the reynolds stress in transferring energy from the shearing mean flow to the acoustic waves. Such action of the reynolds stress can be neglected in ordinary acoustics when the acoustic medium is not moving at speeds comparable to the speed of sound in the medium. However, this action is of crucial importance in the aerodynamic noise of high-speed turbulent jets where the reynolds stress is the fundamental element of the radiating quadrupoles, according to lighthill. Those acoustic waves that become /stationary/ with respect to the local mean flow somewhere in the interior of the shear layer are significantly modified by the viscous action through the critical layer. The shear layer therefore serves as a selective amplifier of the acoustic waves passing through it. Kinematically, the shear layer brings about the preferred downstream emission.. Dynamically, the shear-layer augmentation significantly increases the polar peak noise level. The acoustic power output per unit solid angle for such downstream emissions augmented by the shear layer (including the polar peak) varies as, predicted by lighthill, but without lighthill's convective corrections. On the other hand, the acoustic power output per unit solid angle nearly normal to the jet, due to the transmitted downstream-propagating waves, varies roughly as. Heating the jet gas increases the shear-layer augmentation and may increase the polar peak noise level by several db. The silencing action of the edge notches and edge teeth may also be interpreted as due apparently to the result of possible distortion of the shear-layer profiles."},
{"url":"cran.html#doc89","title":"An investigation of separated flows, part i: the pressure field.","description":"Charwat, A.F. J. Ae. Scs. 28, 1961, 457. The present article describes an investigation of several types of separated regions such as blunt-base wakes and cavities formed in cutouts in the boundaries and ahead of or behind two dimensional steps in supersonic (mach numbers 2 to 4) and subsonic flow. The conditions for the existence, the geometry, and the pressure field are described in this paper. A second article (to be published) will describe investigations of the internal flow and the heat transfer across such separated regions. It is found that there is a maximum (critical) ratio of the length of the separated free-shear layer to the depth of the depression in the boundary beyond which the cavity collapses, leaving mutually independent separated regions at each protrusion. This critical length changes greatly upon laminar-turbulent transition in the oncoming boundary layer,. In either laminar or turbulent flow it is approximately independent of mach and reynolds numbers. A semiempirical correlation predicting the conditions under which the flow will span a depression of arbitrary depth is proposed. Detailed pressure distributions along the boundaries of a cavity (in turbulent flow) are presented as a function of the ratio of the cavity length to the critical length, which is found to be the pertinent similarity parameter. For short notches the impact pressure due to the reversal of the inner portion of the shear layer at recompression tends to thicken the shear layer and a type of boundary layer-free stream interaction governs the pressure field. The pressure in the cavity is nearly constant and can be higher than free-stream. In long notches the shear layer bends inward at separation and curves back gradually ahead of the recompression point. The floor-pressure variation is pronounced and the recovery pressure at reattachment is small. The variation of the drag coefficient with mach number reflects the change from one to the other mechanism of recompression. Detailed surveys of the mach-number distributions in a blunt-body wake and the mixing region behind its throat, as well as in the shear layer spanning a cutout in a wall, are presented and analyzed. It is found that, in general, the assumptions of the simple supersonic-wake models which rely on a principle of steady flow with mass conservation in the cavity are not adequate for cavities in which there is recompression against a boundary. Results showing the influence of the thickness of the initial boundary layer (in the range of 0.3 to 3 times the notch depth) and of the geometry of the notch are also presented."},
{"description":"Chapman, D.R. Nasa r-55, 1959. An analysis is presented of supercircular entry into a planet's atmosphere giving particular attention to the corridor through which spacecraft must be guided in order to accomplish various maneuvers. A dimensionless parameter based on conditions at the conic perigee altitude is introduced for characterizing supercircular entries and conveniently prescribing corridor widths associated with elliptic, parabolic, or hyperbolic approach trajectories. The analysis applies to vehicles of arbitrary weight, shape, and size. Illustrative calculations are made for venus, earth, mars, jupiter, and titan. For nonlifting vehicles having fixed aerodynamic coefficients, curves are presented of dimensionless parameters from which can be calculated the maximum deceleration, maximum rate of laminar convective heating, and total laminar heat absorbed during single-pass entry at velocities up to twice circular velocity. For lifting vehicles, curves are presented of the maximum deceleration and overshoot boundary of an entry corridor,. Equations are presented for estimating laminar aerodynamic heating from the maximum deceleration. It is shown that the corridor width is independent of vehicle weight, dimensions, and drag coefficient, provided these are the same at the overshoot boundary as at undershoot. The corridors of certain planets can be broadened markedly by the application of aerodynamic lift,. For example, the 10-earth-g corridor width for single-pass, nonlifting, parabolic entry is increased from to 52, 51, and 52 miles, respectively, by employing a lift-drag ratio of 1. The use of aerodynamic lift does not increase appreciably the corridors of mars and titan. All corridor widths decrease rapidly as the entry velocity is increased. Terminal guidance requirements on accuracy of velocity and flight path angle for successfully entering various corridors are compared with analogous requirements for putting a satellite into orbit, for hitting the moon from the earth, and for achieving icbm accuracy. Consideration is given to the terminal guidance problem involved in using a planet's atmosphere--rather than rocket fuel--to effect orbital transfers from heliocentric to planeto-centric motion, thereby converting a hyperbolic approach trajectory to an elliptic orbit about the target planet. This fuel saving maneuver appears technologically feasible for certain planetary voyages, and implies the possibility of achieving a large reduction in required earth lift-off weight of chemical propulsion systems.","title":"An analysis of the corridor and guidance requirements for supercircular entry planetary atmospheres.","url":"cran.html#doc163"},
{"url":"cran.html#doc962","title":"Contributions to the theory of heat transfer through a laminar boundary layer.","description":"M. J. Lighthill Department of mathematics, university of manchester communicated by S. Goldstein, F.R.S. An approximation to the heat transfer rate across a laminar incompressible boundary layer, for arbitrary distribution of main stream velocity and of wall temperature, is obtained by using the energy equation in von mises's form, and approximating the coefficients in a manner which is most closely correct near the surface. The heat transfer rate to a portion of surface of length l breadth is given as where k is the thermal conductivity of the fluid, o its prandtl number, p its density, u its viscosity, r(x) is the skin friction, and t(x) the excess of wall temperature over main stream temperature. A critical appraisement of the formula indicates that it should be very accurate for large, but that for of order 0.7 (for most gases) the constant should be replaced by 0.73, when the error should not exceed this yields a formula for nusselt number in terms of the reynolds number r and the mean square root of the skin friction coefficient c, in the case of uniform wall temperature. However, for the boundary layer with uniform main stream, the original formula is accurate to within 3 percent even for. By known transformations an expression is deducted for heat transfer to a surface, with arbitrary temperature distribution along it, and with a uniform stream outside it at arbitrary mach number (equation (42)). From this the temperature distribution along such a surface is deduced in the case (of importance at high mach numbers) when heat transfer to it is balanced entirely by radiation from it. This calculation, which includes the solution of a non-linear integral equation, gives higher temperatures near the nose, and lower ones farther back (figure 2), than are found from a theory which assumes the wall temperature uniform and averages the heat transfer balance. This effect will be considerably mitigated for bodies of high thermal conductivity., the author is not in a position to say whether or not it will be appreciable for metal projectiles. But for stony meteorites at a certain stage of their flight through the atmosphere it indicates that melting at the nose and re-solidification farther back may occur, for which the shape and constitution of a few of them affords evidence. An appendix shows how the method for approximating and solving von mises's equation could be used to determine the skin friction as well as heat transfer rate, but this line seems to have no advantage over established approximate methods."},
{"description":"Taylor, G.I. Proc. Roy. Soc. A, 201, 1950, 159. This paper was written early in 1941 and circulated to the civil defence research committee of the ministry of home security in june of that year. The present writer had been told that it might be possible to produce a bomb in which a very large amount of energy would be released by nuclear fission--the name atomic bomb had not then been used--and the work here described represents his first attempt to form an idea of what mechanical effects might be expected if such an explosion could occur. In the then common explosive bomb mechanical effects were produced by the sudden generation of a large amount of gas at a high temperature in a confined space. The practical question which required an answer was.. Would similar effects be produced if energy could be released in a highly concentrated form unaccompanied by the generation of gas.qm this paper has now been declassified, and though it has been superseded by more complete calculations, it seems appropriate to publish it as it was first written, without alteration, except for the omission of a few lines, the addition of this summary, and a comparison with some more recent experimental work, so that the writings of later workers in this field may be appreciated. An ideal problem is here discussed. A finite amount of energy is suddenly released in an infinitely concentrated form. The motion and pressure of the surrounding air is calculated. It is found that a spherical shock wave is propagated outwards whose radius r is related to the time t since the explosion started by the equation where is the atmospheric density, e is the energy released and s a calculated function of, the ratio of the specific heats of air. The effect of the explosion is to force most of the air within the shock front into a thin shell just inside that front. As the front expands, the maximum pressure decreases till, at about 10 atm., the analysis ceases to be accurate. At 20 atm. 45 of the energy has been degraded into heat which is not available for doing work and used up in expanding against atmospheric pressure. This leads to the prediction that an atomic bomb would be only half as efficient, as a blast-producer, as a high explosive releasing the same amount of energy. In the ideal problem the maximum pressure is proportional to r, and comparison with the measured pressures near high explosives, in the range of radii where the two might be expected to be comparable, shows that these conclusions are borne out by experiment.","title":"The formation of a blast wave by a very intense explosion.","url":"cran.html#doc262"},
{"description":"Chen, C.F. And Clarke, J.H. J. Ae. Scs. 1961, 547. An investigation is made of supersonic-aircraft configurations composed of a cambered body positioned a certain distance beneath an arbitrary lifting wing. The geometry of the wing is regarded as given and the geometry of the body may be given or optimum. Expressions for the drag and lift are obtained from reverse-flow considerations,. These greatly implement such a study when interference cross flows must be cancelled. The drag advantage to be gained when a given body and wing assume a given orientation is studied. Treated more extensively is the variational problem of determining the optimum wing incidence and optimum body shape, for the given volume and length, to yield the minimum drag for prescribed lift. Numerical results are provided to indicate the significance of the large number of parameters appearing in the problem. Of these, the gap between the wing and the body is found to be particularly important. It is found that at low gap moderate body distortions have a significant influence on the drag. Drag reductions of up to 44 relative to the case of no interference have been found at a mach number of 2.24 in a configuration having a gap approximately equal to the maximum diameter of the body, and a wing chord of about three eighths of the length of the body. Comparison is made with the conventional wing-body combination including the effects of skin friction, and it is concluded that the advantage suggested by the preceding considerations is not appreciably diminished. Finally, it is shown that the configurations studied lead to bodies of fineness ratios much lower than are appropriate to conventional wing-body combinations. Tests were made on an arrangement consisting of a scars-haack body located under a lifting rectangular diamond-profile wing. The mach number was 1.6 and the reynolds number was 9.17 x 10 based on the body length. It was found that the measured lift developed on the wing due to the flow field of the body agrees very well with the theoretical value. Downstream of the impinging shock from the wing, flow separation was observed on the exterior of the body but not in the interior. The separation is attributed not to the pressure rise across the shock but to the pressure field arising from the reflection from the body of the shock-induced cross flow. Further observations suggest that the separation can be avoided by pitching the body or by kinking the body at the shock wave to accommodate the shock-induced cross flow.","url":"cran.html#doc1239","title":"Body under lifting wing."},
{"description":"Waldman, G.D. And Probstein, R.F. J. Ae. Scs. 1961, 119. The problem is considered of calculating approximately the inviscid rotational flow field and pressure distribution about a smooth two-dimensional airfoil with sharp leading and trailing edges in a uniform supersonic or hypersonic stream. The assumption of a perfect gas is made, and the basic flow pattern for the analysis is taken to be given by the simple isentropic shock-expansion method with straight characteristics. An elementary characteristics treatment is discussed to show when the simple shock-expansion method should be satisfactory for computing the surface pressure distribution, and under what circumstances it may be expected to break down. By utilizing characteristic variables the isentropic shock-expansion method is then formulated analytically, and an analytic result is obtained for the shock shape corresponding to this zero-order approximation. In the special case where hypersonic similitude is applicable, that is, for slender bodies and high mach numbers, the shock-shape expression for large distances is found to reduce to the result previously given by mahony, which for weak shocks and slender bodies in turn reduces to the simple-wave result first given by friedrichs. Employing the analytic form of the isentropic shock-expansion method as a zero-order approximation, an analytically consistent perturbation method is developed by expanding the dependent flow variables in the exact partial differential equations in powers of the reflection coefficient for simple waves interacting with an oblique shock. The scheme by its nature helps to define those regions in which shock expansion can be used, in addition to taking into account in a perturbation sense the factors neglected in simple shock-expansion theory, namely, the curvature and reflection of the mach waves and the correct boundary conditions at the shock wave. Analytic solutions are obtained for the first-order corrections, including the surface pressure distribution. The necessary numerical computation of the integrals involved is considerably simpler than a direct application of the method of characteristics. To illustrate the method and its accuracy, the zero-order shock shape and first-order pressure distribution are calculated for a family of parabolic arc airfoils at an infinite free-stream mach number. These results are compared with rotational characteristic solutions where available, and the present method is found to be in excellent agreement.","title":"An analytic extension of the shock-expansion method.","url":"cran.html#doc1248"},
{"description":"Chapman, D. And Rubesin, M. J. Ae. Scs. 16, 1949, 547. An analysis is presented which enables the temperature profiles, veiocity profiles, heat transfer, and skin friction to be calculated for laminar flow over a two-dimensional or axially symmetric surface without pressure gradient but with an arbitrary analytic distribution of surface temperature. The general theory is applicable to a gas of any prandtl number, although the numerical results given herein have been computed for air. The predictions of the theory for the special case of constant surface temperature are compared with the calculations of crocco. On the basis of this comparison, it is inferred that the present theory enables heat-transfer and skin-friction calculations accurate to within about 5 per cent to be made for flight conditions up to mach numbers near 5 and to within about 1 or 2 per cent for supersonic wind-tunnel conditions up to considerably higher mach numbers. A particular effort has been made to present the results, which are simple considering their generality, in a form that can be used readily in practical applications. From the mathematical point of view, the theory is applicable to an arbitrary analytic distribution of surface temperature, but in any given practical case it is necessary that the surface-temperature distribution be approximated by a polynomial. The only unknowns in the final equations developed are the coefficients of this polynomial, so that the work involved in applying the theory in any given case depends entirely on the work involved in approximating a given surface- temperature distribution by a polynomial. An example is worked out in detail which illustrates some of the principal effects of variable surface temperature. It is shown that both positively infinite and negatively infinite heat-transfer coefficients can occur. The anomaly of infinite and negative heat-transfer coefficients is discussed and attributed to the customary definition of the heat-transfer coefficient, which is shown to be fundamentally inappropriate for flows with variable surface temperature. In the particular example considered, a conventional method for calculating the net heat transferred yields completely incorrect results. A brief qualitative discussion of the possible effects of the heat transfer on flow separation is given. In order to facilitate the use of the results, all of the principal equations developed are collected and summarized in the section entitled /practical use of results./","url":"cran.html#doc49","title":"Temperature and velocity profiles in the compressible laminar boundary layer with arbitrary distribution of surface temperature."},
{"url":"cran.html#doc344","title":"Some experimental techniques in mass transfer cooling.","description":"Leadon, B.M. Aero/space eng. 18, 1959. Author introduces his survey by a brief review of the history of investigations dealing with boundary layers on impermeable solid surfaces, and notes that no true theory exists for turbulent boundary layers, the success of studies in this area having been due to the introduction of artificial, if ingenious, assumptions which permitted empirical correlations fd data. The terminology introduced by the author for distinguishing the different situations involving mass transfer from the wall to the stream may give rise to some objections. For instance, /film cooling/ need not refer only to the injection of a liquid, since applications involving gas film cooling exist. Also, his restriction of the term /transpiration cooling/ to refer to the injection through a porous surface of a gas only of the same composition as the exterior stream does not enjoy universal usage. The influence of mass transfer on heat transfer through laminar boundary layers and on the transition from laminar to turbulent flow is described, with consideration given to the question of the net effect of the stabilizing influence of surface cooling and the destabilizing influence of injection. Reviewer suggests that author's inaccurate statement to the effect that /thus far the higher energy conditions do not threaten to involve turbulent injection, so turbulent boundary-layer research enjoys a fairly academic serenity broken only by its own frustrations/ be excused on grounds of poetic license, although it ignores the efforts being devoted to the pressing practical problems of erosive burning of solid propellants (possibly the most common example of a complete /aerothermochemical/ problem involving distributed surface heat and mass transfer with chemical reaction in a flow system) and of effusion cooling of rocket nozzles, both of which involve turbulent boundary-layer conditions. Author emphasizes the tedious experimental problems involved in research on boundary layers with blowing, and notes the desirability of velocity distribution measurements, especially in turbulent injection layers. The observation that no good data on concentration profiles in the case of the diffusion boundary layer have been published may be an overstatement, since author's bibliography overlooks the work of J. Berger (/contribution a l'etude de l'injection parietale, / doctor's thesis, university of paris, memorial des poudres 38 (annex), P. 1,. Paris, imprimerie nationale, 1956)."},
{"description":"Cheng, H.K., hall, J.G., golian, T.C. And Hertzberg, A. J. Aero. Sc. V. 28, pp 353-381, 410. 1961. Two important features of hypersonic flow over slender or thin bodies are the displacement effect of the boundary layer and the large down-stream influence of leading-edge bluntness. The present paper contributes new theoretical and experimental results on this problem. The interaction of the two effects is treated theoretically by extending the basic shock-layer concept. In the outer inviscid flow, a model consisting of a detached shock layer and an entropy layer is introduced to account for bluntness. In the boundary layer, the approximate solution is found to be governed by a local flat-plate similarity. Under the assumption of a strong bow shock and a specific heat ratio close to unity, a theory is developed for an arbitrary thin body. For flat-plate afterbodies, the theory yields a solution agreeing with blast-wave theory at one limit and strong-interaction theory at the other. Within the framework of the present theory, the problems involving angle of attack are also analyzed. Complementary to the above study, a hypersonic similitude involving strong shocks, but not requiring close to one a natural comparison with experimental data correlated on the basis of this similitude. Flat-plate experiments in air, conducted in the C.A.L. 11 x 15-dashin. Hypersonic shock tunnel under cold-wall conditions, included measurement of surface heat-transfer distributions and schlieren studies for zero and nonzero angle of attack. Steady laminar heat-transfer rates were measured by means of thin-film resistance thermometers at air test-flow mach numbers around 12, free-stream reynolds numbers from 1.4 x 10 to 1. For most of the experiments, airflow stagnation temperatures ranged from ratios of about 0.15. The range of test conditions at this stagnation temperature encompassed the limiting cases of dominant bluntness and dominant viscous-interaction effects. Heat-transfer distributions were also measured on a sharp plate for air stagnation temperatures ranging from 2, 000degreek up to 4, 000degreek. The experimental data are quite well correlated in terms of the foregoing theoretical similitude variables characterizing combined effects of boundary-layer displacement and bluntness. The correlations obtained suggest that for the present experimental conditions, at least, the hypersonic viscous similitude is valid even with leading-edge bluntness in the paper, is generally fair.","title":"Boundary layer displacement and leading edge bluntness effects in high temperature hypersonic flow.","url":"cran.html#doc572"},
{"description":"Be described here is attributed to the russian investigator V. G. Galerkin, whose original papers are inaccessible to the present writer. His knowledge of the method is derived from a description given in a paper by E. P. Grossman. Grossman states that the method was given by galerkin in his treatise P. 897), and that applications to oscillation problems were first made by V. P. Lyskov. It is pointed out by grossman that galerkin's process in applications to mechanics leads to the same results as lagrange's principle of virtual work, but employs a special co-ordinate system. The method of galerkin belongs to the same general class as those of rayleigh and ritz, for it seeks to obtain an approximate solution of a differential equation with given boundary conditions by taking a function which satisfies these conditions exactly, and proceeds to specialise the function in such a manner as to secure approximate satisfaction of the differential equation. The selected function is a linear combination of n independent functions, and the coefficients are determined by a process of integration. The galerkin process can be considered from two points of view, (a) simply as a means for the approximate solution of differential equations, and treatment of problems concerning the statics and dynamics of elastic and other deformable bodies. These two aspects are treated separately in parts 1 and 2 of the paper respectively, and will now be briefly discussed. Which satisfies the boundary conditions, in the differential equation be. Since the result should be zero, is the error in the differential equation. Then the galerkin process consists in choosing the n coefficients in the function in such a manner that n distinct weighted means of the error, taken throughout a certain range of representation, shall all be zero. As a generalised force, and the multipliers used to weight the errors are the virtual displacements corresponding to increments of each of the generalised co-ordinates in turn. Thus the vanishing of the weighted mean is here interpreted as the vanishing of the virtual work in the appropriate displacement. The degree of accuracy attaindd can be increased indefinitely by increasing the number of independent functions employed, but this entails a great increase of labour. However, when the functions are well chosen, an excellent approximation can be obtained by the use of a very small number, as is sufficiently shown by the examples included in this paper.","url":"cran.html#doc1047","title":"The bending strength of pressurized cylinders."},
{"description":"Ashley, H. And Zartarian, G. J. Ae. Scs. 23, 1956, 1109. Representative applications are described which illustrate the extent to which simplifications in the solutions of high-speed unsteady aeroelastic problems can be achieved through the use of certain aerodynamic techniques known collectively as /piston theory./ based on a physical model originally proposed by hayes and lighthill, piston theory for airfoils and finite wings has been systematically developed by landahl, utilizing expansions in powers of the thickness ratio and the inverse of the flight mach number M. When contributions of orders and are negligible, the theory predicts a point-function relationship between the local pressure on the surface of a wing and the normal component of fluid velocity produced by the wing's motion. The computation of generalized forces in aeroelastic equations, such as the flutter determinant, is then always reduced to elementary integrations of the assumed modes of motion. Essentially closed-form solutions are given for the bending- torsion and control-surface flutter properties of typical section airfoils at high mach numbers. These agree well with results of more exact theories wherever comparisons can be fairly made. Moreover, they demonstrate the increasingly important influence of thickness and profile shape as m grows larger, a discovery that would be almost impossible using other available aerodynamic tools. The complexity of more practical flutter analyses-E.G., on three-dimensional wings and panels-is shown to be substantially reduced by piston theory. An iterative procedure is outlined, by which improved flutter eigenvalues can be found through the successive introduction of higher-order terms in and. Other applications to unsteady supersonic problems are reviewed, including gust response and rapid maneuvers of elastic aircraft. Steady-state aeroelastic calculations are also discussed, but for them piston theory amounts only to a slight modification of ackeret's formulas. Suggestions are made regarding future research based on the new aerodynamic method, with particular emphasis on areas where computational labor can be reduced with a minimum loss of precision. It is pointed out that a mach number zone exists where thermal effects are appreciable but nonlinear viscous interactions may be neglected, and that in this zone piston theory is the logical way of estimating air loads when analyzing aerodynamic- thermoelastic interaction problems.","url":"cran.html#doc14","title":"Piston theory - a new aerodynamic tool for the aeroelastician."},
{"description":"Marble, F. And Adamson, T.C. Jet prop. 24, 1954, 85. The analytic investigation of laminar combustion processes which are essentially two- or three-dimensional present some mathematical difficulties. There are, however, several examples of two-dimensional flame propagation which involve transverse velocities that are small in comparison with that in the principal direction of flow. Such examples occur in the problem of flame quenching by a cool surface, flame stabilization on a heated flat plate, combustion in laminar mixing zones, etc. In these cases the problem may be simplified by employing what is known in fluid mechanics as the boundary-layer approximation, since it was applied first by prandtl in his treatment of the viscous flow over a flat plate. Physically it consists in recognizing that if the transverse velocity is small, the variations of flow properties along the direction of main flow are small in comparison with those in a direction normal to the main flow. The analytic description of the problem simplifies accordingly. The present analysis considers the ignition and combustion in the laminar mixing zone between two parallel moving gas streams. One stream consists of a cool combustible mixture, the second is hot combustion products. The two streams come into contact at a given point and a laminar mixing process follows in which the velocity distribution is modified by viscosity, and the temperature and composition distributions by conduction, diffusion, and chemical reaction. The decomposition of the combustible stream is assumed to follow first-order reaction kinetics with temperature dependence according to the arrhenius law. For a given initial velocity, composition, and temperature distribution, the questions to be answered are.. (1) does the combustible material ignite,. And (2) how far downstream of the initial contact point does the flame appear and what is the detailed process of development. Since the hot stream is of infinite extent, it is found that ignition always takes place at some point of the stream. However, when the temperature of the hot stream drops below a certain value, the distance required for ignition increases so enormously that it essentially does not occur in a physical apparatus of finite dimension. The complete development of the laminar flame front is computed using an approximation similar to the integral technique introduced by von karman into boundary layer theory.","title":"Ignition and combustion in a laminar mixing zone.","url":"cran.html#doc1072"},
{"url":"cran.html#doc193","title":"A study of inviscid flow about air foils at high supersonic speeds.","description":"Eggers, A.J., syvertson, C.A., and krqus, S. Naca report 1123 Steady flow about curved airfoils at high supersonic speeds is investigated analyticially. With the assumption that air behaves as a diatomic gas, it is found the the shock-expansion method may be used to predict the flow about curved airfoils up to extremely high mach numbers, provided the flow deflection angles are not too close to those corresponding to shock detachment. This result applies not only to the determination of the surface pressure distribution, but also to the determination of the whole flow field about an airfoil. Verification of this observation is obtained with the aid of the method of characteristics by extensive calculations of the pressure gradient and shock-wave curvature at the leading edge, and by calculations of the pressure distribution on a 10-percent-thick biconvex airfoil at 0 angle of attack. An approximation to the shock-expansion method for thin airfoils at high mach numbers is also investigated and is found to yield pressures in error by less than 10 percent at mach numbers above three and flow deflection angles up to 25. This slender-airfoil method is relatively simple in form and thus may prove useful for some engineering purposes. Effects of caloric imperfections of air manifest in disturbed flow fields at high mach numbers are investigated, particular attention being given to the reduction of the ratio of specific heats. So long as this ratio does not decrease appreciably below to include the effects of these imperfections, should be substantially as accurate as for ideal-gas flows. This observation is verfied with the aid of a generalized shock-expansion method and a generalized method of characteristics employed in forms applicable for local air temperatures up to about 5000 rankine. The slender-airfoil method is modified to employ an average value of the ratio of specific heats for a particular flow field. This simplified method has essentially the same accuracy for imperfect-gas flows as its counterpart has for ideal-gas flows. An approximate flow analysis is made at extremely high mach numbers where it is indicated that the ratio of specific heats may approach close to 1. In this case, it is found that the shock-expansion method may be in considerable error,. However, the busemann method for the limit of infinite free-stream mach number and specific-heat ratio of 1 appears to apply with reasonable accuracy."},
{"description":"Lees, L. And Hromas, L. J. Ae. Scs. 29, 1962, 976. At reynolds numbers greater than about 5 x 10 corresponding to altitudes below about 180, 000 ft, the hot outer inviscid wake behind the bow shock wave produced by a blunt-nosed body at hypersonic speeds is cooled mainly by turbulent diffusion and conduction. Turbulence originates in the inner wake formed by the coalescence of the free shear layers (or annulus) shed from the body surface when the boundary layer separates from the surface. As this turbulence spreads outward, it swallows enthalpy or momentum defect originally contained in the outer inviscid wake. If the turbulence is locally similar--I.E., if it behaves at each station like a slice of a low-speed /self-similar/ wake--then the turbulent diffusivity grows from a low initial value near the body to a value corresponding to the total drag of the body at about 300 body diameters downstream. At flight velocities of the order of 9, 000-10, 000 ft per sec. The growth of the turbulent inner wake predicted on the basis of locally similar turbulence is in good agreement with shadowgraph measurements of wake widths behind spheres obtained in ballistic ranges in the region from 200 to 4, 000 body diameters downstream of the body. Tentatively, one concludes that the turbulence mechanism in the wake with respect to a fixed observer is similar to the low-speed case, in spite of the large mean temperature gradients. In order to illustrate the behavior of an observable such as electron density in a turbulent wake behind a blunt body, the two limiting cases of thermodynamic equilibrium and pure diffusion (zero electron-ion recombination rate) are calculated for m = 22 at altitudes of 100, 000 and 200, 000 ft. Even for the case of thermodynamic equilibrium, the predicted turbulent radar trail length is about 200 body diameters at l-band (1, 300 mc) at 100, 000-ft altitude and about 150 body diameters for uhf (400 mc) at 200, 000 ft. One interesting result is that the width of the plasma cylinder corresponding to the plasma requency at l-band remains virtually constant at about 3.5 body diameters in the range 30 150 at 100, 000-ft altitude. These results are sufficiently encouraging that one can consider including the effects of finite chemical and electron-ion recombination rates in the analysis in order to give a more complete picture of the wake at hypersonic speeds.","url":"cran.html#doc976","title":"Turbulent diffusion in the wake of a blunt nosed body at hypersonic speeds."},
{"title":"Skin-friction measurements in incompressible flow.","url":"cran.html#doc165","description":"Smith, D.W. And Walker, J. H. Naca report r-26 Experiments have been conducted to measure in incompressible flow the local surface-shear stress and the average skin-friction coefficient for a turbulent boundary-layer on a smooth flat plate having zero pressure gradient. The local surface-shear stress was measured by a floating-element skin-friction balance and also by a calibrated total head tube located on the surface of the test wall. The average skin-friction coefficient was obtained from boundary-layer velocity profiles. The boundary-layer profiles were also used to determine the location of the virtual origin of the turbulent boundary layer. Data were obtainec for a range of reynolds numbers from 1 million to about 45 million with an attendant change in mach number from 0.11 to 0.32. The measured local skin-friction coefficients obtained with the floating-element balance agree well with those of schultz-grunow and kempf for reynolds numbers up to 45 million. The measured average skin-friction coefficients agree with those given by the schoenherr curve in the ranges of reynolds numbers from 1 to 3 million and 30 to 45 million. In the range of reynolds numbers from 3 to 30 million the measured values are less than those predicted by the schoenherr curve. The results show that the /univeral skin-friction constants/ proposed by coles appraoch asymptotically a constant value at reynolds numbers exceeding mentioned constants and the limited reynolds number range of the present investigation, there is some doubt as to the validity of any turbulent skin-friction law written on the basis of the present results. Hence, no new friction law is proposed. The frictional resistance of a flat plate was calculated by means of the momentum method and also the integrated measured local surface shear. For reynolds numbers from 14 million to 45 million both methods give about the same result,. Whereas at lower values of reynolds number the momentum method based on velocity profiles uncorrected for the effects of turbulence results in a frictional resistance as much as 4 percent higher than that of the integrated shear. The measurement of local surface shear by a calibrated preston tube appears to be accurate and inexpensive. The calibration as given by preston must be modified slighlty, however, to yield the results obtained from the floating-element skin-friction balance."},
{"description":"Rogers, A.W. Naca tn.3227, 1954. A theoretical investigation has been made of a general method for predicting the flow field behind the wings of plane and cruciform wing and body combinations at transonic or supersonic speeds and slender configurations at subsonic speeds. The wing trailing-vortex wake is represented initially by line vortices distributed to approximate the spanwise distribution of circulation along the trailing edge of the exposed wing panels. The afterbody is represented by corresponding image vortices within the body. Two-dimensional line-vortex theory is then used to compute the induced velocities at each vortex and the resulting displacement of each vortex is determined by means of a numerical stepwise integration procedure. The method was applied to the calculation of the position of the vortex wake and the estimation of downwash at chosen tail locations behind triangular-wing and cylindrical-body combinations at supersonic speeds. The effects of such geometric parameters as aspect ratio, angle of attack and incidence, ratio of body radius to wing semi-span, and angle of bank on the vortex wake behind wings of wing-body combinations were studied. The relative importance of wing vortices, the corresponding image vortices within the body, and body crossflow indetermining the the total downwash was assessed at a possible tail location. It was found that the line-vortex method of this report permitted the calculation of vortex paths behind wings of wing-body combinations with reasonable facility and accuracy. A calculated sample wake shape agreed qualitatively with one observed experimentally, and sample results of the line-vortex method compared well with an available exact crossflow-plane solution. An empirical formula was derived to estimate the number of vortices required per wing panel for a satisfactory computation of downwash at tail locations. It was found that the shape of the vortex wake and the ultimate number of rolled-up vortices behind a wing depend on the circulation distribution along the wing trailing edge. For the low-aspect-ratio plane wing and body combinations considered, it appeared that downwash at horizontal tail locations is largely determined except near the tail-body juncture by the wing vortices alone for small ratios of body radius to wing semispan, and by the body upwash alone for large values of that ratio.","url":"cran.html#doc433","title":"Application of two dimensional vortex theory to the prediction of flow fields behind wings of wing-body combinations at subsonic and supersonic speeds."},
{"description":"Greensite, A.L. J. Ae. Scs. 29, 1962, 745. Author considers the equation of the yawing motion of a missile, derived with a series of customary assumptions and with the distance traveled as the independent variable. His assumptions include the linearity of the aerodynamic forces, the constancy of the aerodynamic coefficients with respect to mach number, the absence of spin, and the absence of gravity. If to these assumptions one could add the common ballistic assumption of a constant air density, the coefficients of this equation would have been con-damped sinusoids. In ballistics any slow variation of these coefstant, and the solution would have been simply the exponentially-ficients is usually treated by adding an approximate correction term to the damping rate (which is spoken of as the wkb perturbation). However, with a body entering the planetary atmosphere the variation of the air density is apparently of greater essence (this is a point not stated explicitly in this brief communication), and the equation is of the type. The author shows that with a series of further transformations the equation can be reduced to the form the solutions of which are confluent hypergeometric functions. These functions are defined as series involving gamma functions, and with a series of further assumptions can be reduced to laguerre polynomials and bessel functions. It is certainly nice to have an exact solution to a problem which has heretofore been extensively treated by approximations and by the numerical approach. This reviewer is puzzled, however, as to the practical significance of the proposed approach. An idealization is of value in that it facilitates our understanding,. And The numerical approach, in that it allows refinements of the problem, freeing us from the necessity of idealizing. But the proposed solution is certainly more difficult to refine than the original problem,. And It is certainly not simple (the solution of the original equation is not the value of z, but the various /reverse/ transformations of z). An evaluation of a series in practice must compete with the numerical approach,. And The equation suggested is of the zero). Viewing the problem /afresh/ (in the light of the / computer revolution/ and without the constraints imposed by the prior art), it seems at least equally easy to /standardize/ the solutions of the original equation.","url":"cran.html#doc499","title":"A closed-form solution for the oscillations of a vehicle entering a planetary atmosphere."},
{"title":"Investigation of full scale split trailing edge wing flaps with various chords and hinge locations.","url":"cran.html#doc673","description":"Wallace, R. Naca R.539, 1935. An investigation was conducted in the N. A. C. A. Full-scale wind tunnel on a small parasol monoplane equipped with three different split trailing-edge wing flaps. The object of the investigation was to determine and correlate data on the characteristics of the airplane and flaps as affected by variation in flap chord, flap deflection, and flap location along the wing chord. The chords of the flaps were 10, 20, and 30 percent of the wing chord and each flap was tested at deflections from 0 to 75 when located successively at 68, 80, and 88.8 percent of the wing chord aft of the leading edge. The investigation included force tests, pressure-distribution tests, and downwash surveys. The results give the lift, the drag, and the pitching-moment characteristics of the airplane, the flap forces and moments, the pressure distribution over the flaps and wing at one section, and the downwash characteristics of the flap and wing combinations. An increase in flap chord or distance of the flap from the leading edge of the wing increased the lift of the airplane but had an adverse effect on the wing pitching moment. The ld ratio of the airplane decreased with increase in flap deflection or flap chord. Flap normal-force coefficients were primarily a function of flap deflection and were relatively independent of flap chord, hinge-axis location, and airplane attitude. The location of the flap center of pressure in percentage of flap chord aft of the hinge axis remained practically constant irrespective of airplane attitude and of flap deflection, chord, or location. Flap hinge-moment coefficients varied with a power of flap chord greater than the square so that with regard to hinge moments narrow flaps were the most efficient in producing a given increase in lift. Split trailing-edge flaps materially affected the magnitude and distribution of pressures over the entire wing profile. At low angles of attack the predominant effect of the flaps was to increase positively the lower-surface pressures ,. At high angles of attack, to increase negatively the upper-surface pressures. Downwash surveys indicated that horizontal tail planes located above the wing chord line would be more effective than those below the chord in counteracting the increased diving moment of the airplane with flaps deflected."},
{"description":"Libby, pa. And Pallone, A. J. Ae. Scs. 21, 1954. In some cooling problems associated with high energy flows it may be convenient to localize strongly the cooling, as for example by injecting a coolant through an upstream porous strip, and to depend on the insulating properties of the boundary layer to reduce, or to eliminate completely the need for further cooling on the surface downstream of the highly cooled section. This upstream cooling technique may be of interest in connection with optical windows in hypersonic wind tunnels, and on radomes, wings, and bodies of high-speed aircraft and missiles. In this paper a method for investigating the insulating properties of a laminar compressible boundary layer on a two- dimensional surface with zero heat transfer is presented. The physical situation considered thus corresponds to the case in which the heat transfer downstream of the strongly cooled section is completely eliminated. Of practical concern is how the temperature of the uncooled surface varies in the downstream direction from its low initial value and thus how the low energy layer established by the upstream cooling insulates the downstream surface. The karman integral method extended to both the momentum and energy partial differential equations of the boundary layer has been used. The station, at which cooling and or injection ceases, corresponds to a discontinuity in boundary conditions and thus in solutions. At this point the flux of mass, momentum, and energy within the boundary layer has been made continuous by the introduction of three additional parameters in the velocity and stagnation enthalpy profiles. Thus the velocity and stagnation enthalpy profiles have both been taken as sixth degree polynomials. The resulting two integral-differential equations are then solved for two unknown functions of the distance along the wall. These two functions are related to the boundary-layer thickness and to the wall temperature. Initial conditions corresponding to a given initial wall temperature and an initial boundary-layer thickness are prescribed. Exact closed-form solutions for the case of zero axial pressure gradient are obtained. For flows with significant pressure gradients, numerical solutions are required in general. Several numerical examples of practical interest are presented.","title":"A method for analysing the insulating properties of the laminar compressible boundary layer.","url":"cran.html#doc364"},
{"description":"Zakkay, V. And Callahan, C.J. J. Ae. Scs. 29, 1962, 1403. 0. An experimental investigation of the laminar, transitional, and turbulent heat transfer rates over a conical cylindrical flared body is presented. Regions of favorable, zero, and adverse pressure gradient on the body are investigated. The experimental results are compared with the theories available in the literature. The model chosen for this investigation is a cone-cylinder-flare configuration consisting of a 20 semivertex conical nose portion smoothly blended by a shoulder radius into a long cylindrical body and terminated by a smooth large radius flare. The model was tested at a free stream mach number of 8, over a range of reynolds number from 0.3 x 10 to 1.6 x 10 per inch based on free stream conditions. Various stagnation-to-wall temperature ratios were obtained by cooling the model prior to the test with liquid nitrogen. The stagnation-to-wall temperature ratios were 10 and 3.3. The theoretical predictions gave good results for the heat transfer rates in the laminar region, and fair prediction in the transitional and turbulent regimes extending over the shoulder and forward portion of the cylindrical body. Over the aft portion of the cylinder and over the flare the predictions are only qualitatively correct, and underestimate the heating rate by a factor as high as 3. Conversely, the /flat plate reference enthalpy/ over the aft portion of the body, but to increasingly overestimate the heating rates over the forward portion of the cylinder. A modified equation for the heat transfer coefficient in the transitional and fully turbulent region based on the F.P.R.E. Method is then presented. This method gives good agreement with the experimental results presented over the entire range of transitional and turbulent flow. From the results the following is concluded.. Cooling the wall delayed transition. By expanding the flow rapidly between the cone and the cylinder, the transition reynolds number is reached very rapidly. By making a smooth transition between the cylinder and the flare, no separation occurred at the cylindrical flare junction. The transitional and turbulent heat transfer in the presence of an adverse pressure gradient may be predicted with sufficient accuracy by the F.P.R.E. Method.","title":"Laminar, transitional and turbulent heat transfer to a cone-cylinder-flare body at mach 8. 0.","url":"cran.html#doc522"},
{"title":"Inviscid hypersonic flow over blunt-nosed slender bodies.","url":"cran.html#doc25","description":"Lees, L. And Kubota, T. J. Ae. Scs. 24, 1957, 195. At hypersonic speeds the drag area of a blunt nose is much larger than the drag area of a slender afterbody, and the energy contained in the flow field in a plane at right angles to the flight direction is nearly constant over a downstream distance many times greater than the characteristic nose dimension. The transverse flow field exhibits certain similarity properties directly analogous to the flow similarity behind an intense blast wave found by G. I. Taylor, S. C. Lin, and A. Sakurai. A comparison with the experiments of hammitt, vas, and bogdonoff on a flat plate with a blunt leading edge at in helium shows that the shock-wave shape is predicted very accurately by this similarity analysis. The predicted surface pressure distribution is somewhat less satisfactory. Experimental results on a hemisphere-cylinder obtained at in the galcit air tunnel indicate that not only the shock-wave shape but also the surface pressures for this body are given very closely by the similarity theory, except near the hemisphere-cylinder junction. Energy considerations combined with a detailed study of the equations of motion show that flow similarity is also possible for a class of bodies of the form, provided that, where for a two-dimensional body and for a body of revolution. When the shock shape is not similar to the body shape, and the entire flow field some distance from the nose must depend to some extent on the details of the nose geometry. By again utilizing energy and drag considerations one finds that at hypersonic speeds the inviscid surface pressures generated by a blunt leading edge are larger than the pressures induced by boundary-layer growth on an insulated flat surface for an insulated blunt-nosed slender body of revolution the corresponding distance is given by. (here is free-stream reynolds number based on leading-edge thickness, or nose diameter.) in free flight these constants are replaced by 1, 700 and 20, respectively, so that viscous interaction effects are important over the forward portion of a blunt- nosed slender body only for relatively low values of. However, /far downstream/ of the nose the inviscid over-pressure is small and viscous interaction phenomena will have to be taken into account."},
{"description":"Wight, K.C. Part i, arc r + m 2934, 1955. Part ii arc r + m 3029, 1958. Measurements have been made of the direct two-dimensional damping and stiffness derivatives for a in incompressible flow. Corrections arising from the apparatus are discussed and reference is made to an attempt to measure the direct tab derivatives. The effects are shown of frequency parameter, amplitude of oscillation, reynolds number, aileron angle and position of transition on the wing. Variation with frequency parameter is substantially the same as for vortex-sheet theory and variation of amplitude produces little change in both derivatives. At the lowest reynolds number there is little change in both derivatives with variation of aileron angle for the condition of natural transition, but at higher reynolds numbers the stiffness derivatives increase at. A forward movement of transition reduces the stiffness derivatives at the smaller aileron angles, but at, at the lowest reynolds number, an increase results. Similar trends are observed for the damping derivatives above. Comparison with vortex-sheet theory shows that the measured values of the stiffness and damping derivatives are approximately 0.6 of the theoretical values. Measurements have been made of the direct tab derivatives and cross aileron-tab derivatives for a per cent aileron and 4 per cent (approx.) tab. In addition some measurements of the direct aileron derivatives have been made for comparison with earlier results together with a number of static derivatives for the wing and controls. The influence is shown of frequency parameter, reynolds number, position of transition, mean tab angle and sealing of the control hinge gaps. Some tests have been made with the ailcron set at minus 8 deg and the tab at plus 12 deg for which condition the hinge moment on the aileron was zero. Reasonable agreement with the values given by the /equivalent profile/ theory is shown for both direct damping derivatives and for the direct tab stiffness derivative. The direct aileron stiffness derivative shows some departure from the theoretical value when. At and the natural transition, comparison with the values given by flat-plate theory gives the following approximate factors, where suffix denotes the theoretical values..","title":"Measurement of two dimensional derivatives on a wing-aileron-tab system.","url":"cran.html#doc199"},
{"description":"Mirels, H. Nasa r-15, 1959. Approximate analytical solutions are presented for two-dimensional and axisymmetric hypersonic flow over blunt-nosed slender bodies whose shapes follow a power law variation. In particular, the body shape is given by where is the transverse body ordinate, is the streamwise distance from the nose, and m is a constant in the range. Both zero-order solutions and first-order (small but nonvanishing values of solutions are presented, where m is the free-stream mach number and is a characteristic body or streamline slope. The zero-order shock shape is similar to the body shape for these flows. The solutions are found within the framework of hypersonic-slender-body theory. The limiting case m=1 corresponds to a wedge or cone flow. The limiting case corresponds to a constant-energy flow. The latter cases are included so that the present study may be applied to all flows wherein the zero-order shock shape is given by with m in the range. Flow fields associated with shock shapes having values of m outside this range are also discussed. For all values of, except m=1, certain portions of the flow field riolate the hypersonic-slender-body approximations, while other portions are consistent with these approximations. For m=1, all portions of the flow field are consistent with the approximations. The approximate solutions are found as follows. The asymptotic form of the flow in the vicinity of the body surface is used as a guide to write approximate expressions for the dependent variables. These expressions exactly satisfy the continuity and energy equations and contain arbitrary constants which are evaluated so as to satisfy boundary conditions at the shock. The approximate solutions do not satisfy the lateral momentum equation except at the shock and (for the first-order problem) at the body surface. The results of the approximate solutions are compared with numerical integrations of the equations of motion for various values of m and (ratio of specific heats). Good agreement is noted, particularly when m and are both near one. The shock is relatively close to the body for the latter cases. Sufficient results are presented to evaluate the accuracy of the approximate method for various values of m and.","title":"Approximate analytical solutions for hypersonic flow past slender power-law bodies.","url":"cran.html#doc160"},
{"description":"Jorgensen, L.H. Naca tn4045, 1957 To help fill the gap in the knowledge of aerodynamics of shapes intermediate between bodies of revolution and flat triangular wings, force and moment characteristics for elliptic cones have been experimentally determined for mach numbers of 1.97 and sectional axis ratios from 1 through 6 and with lengths and base areas equal to circular cones of fineness ratios 3.67 and 5 have been studied for angles of bank of 0 and 90. Elliptic and circular cones in combination with triangular wings of aspect ratios 1 and 1.5 also have been considered. The angle-of-attack range was from 0 to about 16, and the reynolds number was 8x10, based on model length. In addition to the forces and moments at angle of attack, pressure distributions for elliptic cones at zero angle of attack have been determined. The results of this investigation indicate that there are distinct aerodynamic advantages to the use of elliptic cones. With their major cross-sectional axes horizontal, they develop greater lift and have higher lift-drag ratios than circular cones of the same fineness ratio and volume. In combination with triangular wings of low aspect ratio, they also develop higher lift-drag ratios than circular cones with the same wings. For winged elliptic cones, this increase in lift-drag ratio results both from lower zero-lift drag and drag due to lift. Visual-flow studies indicate that, because of better streamlining in the crossflow plane, vortex flow is inhibited more for an elliptic cone with major axis in the plane of the wing than for a circular cone with the same wing. As a result, vortex drag resulting from lift is reduced. Shifts in center of pressure with changes in angle of attack and mach number are small and about the same as for circular cones. Comparisons of theoretical and experimental force and moment characteristics for elliptic cones indicate that simple linearized (flat plate) wing theory is generally adequate even for relatively thick cones. Zero-lift pressure distributions and drag can be computed using van dyke's second-order slender-body theory. For winged circular cones, a modification of the slender-body theory of naca rep. 962 results in good agreement of theory with experiment.","url":"cran.html#doc225","title":"Elliptic cones alone and with wings at supersonic speeds."},
{"description":"Turcotte, D.L. J. Ae. Scs.1960. It is generally recognized that stable combustion processes in heated boundary layers may be achieved by either of two conceptual mechanisms. In one mechanism it is pictured that the heat transfer to the wall quenches the propagating flame at a certain distance from the surface. The equality between the flow velocity and the normal burning velocity at this quenching distance determines the position of the propagating flame. In the second mechanism it is conceived that the hot surface provides a continuous source of ignition in much the same manner that the hot recirculation zone of a bluff body flame holder provides continuous ignition to the gas flowing around it. In this case it is the characteristic time during which the gas must be heated that determines the position of the flame. All experimental work reported to date has been concerned with conditions where the first picture has apparently been applicable. In the present paper, experiment and analysis are given that show under what conditions the continuous ignition mechanism provides the appropriate model and also how the two models are related. To differentiate the two mechanisms an experiment was set up to study flame stabilization in high-velocity boundary layers over a wall heated in the form of a step function. With a turbulent boundary layer and a wall temperature above 1, 700f., the characteristic time was found to be a systematic and reproducible variable. These observations led to the conclusion that a continuous ignition mechanism governs stabilization in heated turbulent boundary layers. A rational explanation is made for the transition from the low-speed mechanism known to be applicable in unheated turbulent boundary layers and heated laminar boundary layers to the ignition mechanism applicable in heated turbulent boundary layers. As a further verification of the continuous ignition mechanism an apparent ignition energy was found. The logarithm of the heat added at the lower stability limit was found to be a linear function of the reciprocal of the limiting wall temperature. The activation energy derived from this arrhenius type of relation agreed reasonably well with the estimated value for the fuel used.","url":"cran.html#doc1268","title":"Stable combustion of a high-velocity gas in a heated boundary layer."},
{"description":"Chapman, D.R., wimbrow, W.R. And Kester, R.H. Naca r1109. Measurements of base pressure are presented for 29 blunt-trailing-edge wings having an aspect ratio of 3.0 and various airfoil profiles. The different profiles comprised thickness ratios between 0.05 and 0.10, boattail angles between --2.9 and 20, and ratios of trailing-edge thickness to airfoil thickness between 0.2 and 1.0. The tests were conducted at mach numbers of 1.25, 1.5, 2.0, and 3.1. For each mach number, the reynolds number and angle of attack were varied. The lowest reynolds number investigated was 0.2 x 10 and the highest was 3.5 x 10. Measurements on each wing were obtained separately with turbulent flow and laminar flow in the boundary layer. Span-wise surveys of the base pressure were conducted on several wings. The results with turbulent boundary-layer flow showed only small effects on base pressure of variations in reynolds number, airfoil profile shape, boattail angle, and angle of attack. The principal variable affecting the base pressure for turbulent flow was the mach number. At the highest mach number investigated (3.1), the ratio of boundary-layer thickness to trailing-edge thickness also affected the base pressure significantly. The results obtained with laminar boundary-layer flow to the trailing edge showed that the effect of reynolds number on base pressure was large. In all but a few exceptional cases the effects on base pressure of variations in angle of attack and in profile shape upstream of the base were appreciable though not large. The principal variable affecting the base pressure for laminar flow was the ratio of boundary-layer thickness to trailing-edge thickness. For a few exceptional cases involving laminar flow to the trailing edge, the effects on base pressure of variations in profile shape, boattail angle, and angle of attack were found to be unusually large. In such cases the variation of base pressure with angle of attack was discontinuous and exhibited a hysteresis. Stroboscopic schlieren observations at a mach number of 1.5 indicated that these apparently special phenomena were associated with a vortex trail of relatively high frequency.","title":"Experimental investigation of base pressure on blunt-trailing-edge wings of supersonic velocities.","url":"cran.html#doc189"},
{"description":"Stratford, B.S. And Sansome, G.E. Arc r + m 3275, 1960. In special circumstances where a large work output is required from a turbine in a single stage it is necessary to use high pressure ratios across the nozzle blades, thus producing supersonic velocities at inlet to the rotor. As part of an investigation into such turbines, several designs for the inter-blade passages of the rotor have been tested in a two-dimensional tunnel, a design theory being developed concurrently. The first design, featuring constant passage width and curvature as in steam-turbine practice, but having thin leading and trailing edges, was found to suffer from focusing of the compression waves from the concave surface, with consequent flow separation from the opposite convex surface. It gave a velocity coefficient of measured at an inlet mach number of 1.90 and turning angle of 140 deg. The measured value compares favourably with values from previous steam tests, where the results have been in the range from 0.65 to 0.92. From theoretical reasoning, and from additional test observations, a subsequent passage was designed having an inlet transition length of small curvature, leading to a free-vortex passage of double the transition curvature,. A small amount of contraction was incorporated. Schlieren photographs showed the flow in this passage to be almost shock free. A thin region of low-energy air existed close to the convex surface, but liquid-injection tests located only one small bubble of reversed flow. Pressure traverses at exit indicated a velocity coefficient of 0.952, based on the area-mean total pressure. When allowance is made for turning angle and reynolds number this result appears to compare quite favourably with previous work. It would seem that the optimum blade pitching in a turbine would be about 20 to 30 per cent closer than in a two-dimensional cascade. However, the resultant pitching tends to become very close, except at very large turning angles, with the result that in some applications difficulties could arise in the practical design and manufacture. Several uncertainties remain and the present design must be regarded as still experimental.","title":"Theory and tunnel tests of rotor blade for supersonic turbines.","url":"cran.html#doc212"},
{"description":"Lighthill, M.J. J.fluid mech. 2, 1957, 1. This is a lucid introduction to the effects of dissociation in gas dynamics. The problem in view is that of air flow past a bluff body at speeds somewhat above 2 km sec. Thermodynamic equilibrium is assumed,. Theories of near equilibrium for transport properties and of large departures from equilibrium being promised in parts 2 and 3. Following a survey of the equilibrium statistical thermodynamics of a pure dissociating diatomic gas, a new model is introduced. This /ideal dissociating gas/ is characterized by only three constants, the characteristic temperature, density and internal energy for dissociation. Physically, it may be regarded as having its vibrational modes always just half excited (so that at low temperatures the ratio of specific heats approaches 4 3 rather then 7 5). Thermodynamic properties of the ideal gas are derived, and the oblique shock wave relations deduced in the /strong-shock/ approximation (including an elegant relation between the principal curvatures of any bow shock and the subsequent vorticity). Useful relations are given for the isentropic changes that take place along streamlines between shocks. Various of these results are applied to the problem typified by a sphere flying at high mach number. The newtonian impact theory and its empirical modification are dismissed as lacking theoretical basis, in favor of the limit for large values of both mach number and density ratio across the shock. It is suggested that the zero surface pressure sometimes predicted by the latter theory corresponds to separation not of the flow but of the shock wave from the surface. An estimate is given for the subsequent shape of the shock. Finally, another approximation is applied to the region near the stagnation streamline. The fluid is assumed incompressible, but rotational in accord with the shock relations,. And It is shown that a spherical shock corresponds to a concentric spherical body. The resulting surface pressure is within 1 per cent of that predicted by freeman's second approximation based on the newtonian-plus-centrifugal solution (same J. 1 (1956),","title":"Dynamics of a dissociating gas.","url":"cran.html#doc110"},
{"url":"cran.html#doc131","title":"Two-dimensional jet mixing of a compressible fluid.","description":"Pai, S.I. J.aero.scs. 16, 1949, 463. The mixing and divergence of a supersonic jet exhausting into a supersonic stream are investigated theoretically. In the first part of this paper, the flow is assumed to be laminar. When the velocity and temperature in the jet are different slightly from those of the surrounding stream, by the method of small perturbations and under ordinary boundary layer assumptions, the equation of motion of two-dimensional flow will be reduced to a form of the well-known equation of heat conduction, whose solution is known for any given boundary conditions. It has also been shown that the exact solution of the two dimensional jet mixing of viscous compressible fluids can be obtained by successive approximations starting with the solution of small perturbations. Velocity and temperature distributions for two cases--one is the mixing of two-uniform flows and the other is the mixing of a jet of compressible fluid from a two-dimensional nozzle with full expansion exhausting into a supersonic stream--have been calculated. The properties of the jet mixing depend mainly on the momentum of the jet regardless of whether the change of momentum is due to the change of velocity or the change of temperature--I.E., the change of density. Compressibility has a considerable effect on the properties of the jet. In the second part, the cases of turbulent flow are investigated. By means of reichardt's theory of free turbulence, the turbulent shearing stress may be expressed as it has been shown in this paper that where is a constant that can be determined experimentally. The value of n lies between 0 and 1. The exact value of n depends on the condition of mixing. When the expression of turbulent shearing stress given above is used instead of the viscous stress in the equation of motion, by suitable transformation of variables, it has been shown that the equation of two-dimensional turbulent jet mixing is identical to that of the laminar case. Hence, the solution of the first part of this paper can be applied to the turbulent case, provided that the characteristic constants and n have been properly chosen."},
{"description":"Stine, H.A. And Wanlass, K. Naca tn.3344, 1954. The effect of a strong, negative pressure gradient upon the local rate of heat transfer through a laminar boundary layer on the isothermal surface of an electrically heated, cylindrical body of revolution with a hemispherical nose was determined from wind-tunnel tests at a mach number of 1.97. The investigation indicated that the local heat-transfer parameter, based on flow conditions just outside the boundary layer, decreased from a value of 0.65 0.10 at the stagnation point of the hemisphere to a value of 0.43 0.05 at the junction with the cylindrical afterbody. Because measurements of the static pressure distribution over the hemisphere indicated that the local flow pattern tended to become stationary as the free-stream mach number was increased to 3.8, this distribution of heat-transfer parameter is believed representative of all mach numbers greater than 1.97 and of temperatures less than that of dissociation. The local heat-transfer parameter was independent of reynolds number based on body diameter in the range from 0.6x10 to 2.3x10. The measured distribution of heat-transfer parameter agreed within theoretical distribution calculated with foreknowledge only of the pressure distribution about the body. This method, applicable to any body of revolution with an isothermal surface, combines the mangler transformation, stewartson transformation, and thermal solutions to the falkner-skan wedge-flow problem, and thus evaluates the heat-transfer rate in axisymmetric compressible flow in terms of the known heat-transfer rate in an approximately equivalent two-dimensional incompressible flow. Measurements of recovery-temperature distributions at mach numbers of 1.97 and 3.04 yielded local recovery factors having an average value of 0.823 0.012 on the hemisphere which increased abruptly at the shoulder to an average value of 0.840 0.012 on the cylindrical afterbody. This result suggests that the usual representation of the laminar recovery factor as the square root of the prandtl number is conservative in the presence of a strong, accelerating pressure gradient.","url":"cran.html#doc662","title":"Theoretical and experimental investigation of aerodynamic-heating and isothermal heat transfer parameters on a hemisphere nose with laminar boundary layer at supersonic mach numbers."},
{"url":"cran.html#doc140","title":"The determination of turbulent skin friction by means of pitot tubes.","description":"Preston, J.H. J.roy.ae.S. 58, 1954, 109. A simple method of determining local turbulent skin friction on a smooth surface has been developed which utilises a round pitot tube resting on the surface. Assuming the existence of a region near the surface in which conditions are functions only of the skin friction, the relevant physical constants of the fluid and a suitable length, a universal non-dimensional relation is obtained for the difference between the total pressure recorded by the tube and the static pressure at the wall, in terms of the skin friction. This relation, on this assumption, is independent of the pressure gradient. The truth and form of the relation were first established, to a considerable degree of accuracy, in a pipe using four geometrically similar round pitot tubes--the diameter being taken as representative length. These four pitot tubes were then used to determine the local skin friction coefficient at three stations on a wind tunnel wall, under varying conditions of pressure gradient. At each station, within the limits of experimental accuracy, the deduced skin friction coefficient was found to be the same for each pitot tube, thus confirming the basic assumption and leaving little doubt as to the correctness of the skin friction so found. Pitot traverses were then made in the pipe and in the boundary layer on the wind tunnel wall. The results were plotted in two non-dimensional forms on the basis already suggested and they fell close together in a region whose outer limit represented the breakdown of the basic assumption, but close to the wall the results spread out, due to the unknown displacement of the effective centre of a pitot tube near a wall. This again provides further evidence of the existence of a region of local dynamical similarity and of the correctness of the skin friction deduced from measurements with round pitot tubes on the wind tunnel wall. The extent of the region in which the local dynamical similarity may be expected to hold appears to vary from about to of the boundary-layer thickness for conditions remote from, and close to, separation respectively."},
{"url":"cran.html#doc101","title":"Laminar heat transfer over blunt-nosed bodies at hypersonic flight speeds.","description":"Lester lees The ramo-wooldridge corporation, los angles, and california institute of technology, pasadena, california This paper deals with two limiting cases of laminar heat transfer over blunt-nosed bodies at hypersonic flight speeds, or high stagnation temperatures.. (a) thermodynamic equilibrium, in which the chemical reaction rates are regarded as /very fast/ compared to the rates of diffusion across streamlines., (b) diffusion as rate-governing, in which the volume recombination rates within the boundary layer are /very slow/ compared to diffusion across streamlines. In either case the gas density near the surface of a blunt-nosed body is much higher than the density just outside the boundary layer, and the velocity and stagnation enthalpy profiles are much less sensitive to pressure gradient than in the more familiar case of moderate temperature differences. In fact, in case (a), the nondimensionalized enthalpy gradient at the surface is represented very accurately by the /classical/ zero pressure gradient value, and the surface heat-transfer rate distribution is obtained directly in terms of the surface pressure distribution. In order to illustrate the method, this solution is applied to the special cases of an unyawed hemisphere and an unyawed, blunt cone capped by a spherical segment. In the opposite limiting case where diffusion is rate-controlling the diffusion equation for each species is reduced to the same form as the low-speed energy equation, except that the prandtl number is replaced by the schmidt number. The simplifications introduced in case (a) are also applicable here, and the expression for surface heat transfer rate is similar., the maximum value of the ratio between the rate of heat transfer by diffusion alone and by heat conduction alone in the case of thermodynamic equilibrium is given by.. (prandtl no./schmidt no.) when the diffusion coefficient is estimated by taking a reasonable value of atom-molecule collision cross section this ratio is 1.30. Additional theoretical and (especially) experimental studies are clearly required before these simple results are accepted."},
{"description":"Hall, J.G., eschenroeder, A.W. And Marrone, P.V. Ias paper 62-67, 1962. Analyses have been made of the effects of coupled chemical rate processes in external inviscid hypersonic airflows at high enthalpy levels. Exact (numerical) solutions have been obtained by the inverse method for inviscid airflow over a near-spherical nose under flight conditions where substantial nonequilibrium prevails through the nose region. Typical conditions considered include nose radii of the order of 1 ft at an altitude of 250, 000 ft and velocities of 15, 000 and 23, 000 ft per sec. The results illustrate the general importance of the coupling among the reactions considered. These included dissociation-recombination, bimolecular-exchange, and ionization reactions. The exact solutions show the bimolecular, no exchange reactions to be important in blunt-nose flow for the kinetics of no and n, as they are in the case of a plane shock wave. An important difference between blunt-nose flow and plane shock flow, however, is the gasdynamic expansion in the curved shock layer of the former. This expansion reduces post-shock reaction rates. As a consequence, in the regime studied the oxygen and nitrogen-atom concentrations tend to freeze in the nose region at levels below those for infinite-rate equilibrium. The reduction below the equilibrium dissociation level can be large, particularly for nitrogen dissociation at higher velocities. In the regime considered, the chemical kinetics are dominated by two-body collision processes. The inviscid nose flow, including coupled nonequilibrium phenomena, is thus amenable to binary scaling for a given velocity. The binary scaling is demonstrated for a range of altitude and scale by correlation of the exact solutions for given velocity and a constant product of ambient density and nose radius. This similitude, which can also scale viscous nonequilibrium and radiation phenomena in the shock layer, provides a useful flexibility for hypersonic testing where it is applicable. The afterbody inviscid-flow problem is briefly discussed in the light of the results for the nose flow.","title":"Inviscid hypersonic airflows with coupled non-equilibrium processes.","url":"cran.html#doc401"},
{"description":"Kaplan, A. And Fung, Y.C. Naca tn.3212, 1954. A shallow spherical dome subjected to lateral pressure is a structure for which the deformation departs appreciably from the linear theory at relatively small values of the deflection amplitude. It is also one for which the buckling process is characterized by a rapid decrease in the equilibrium load once the buckling load has been surpassed. For structures having this type of buckling characteristics the question arises as to whether the proper buckling criterion to apply is the classical criterion, which considers equilibrium with respect to infinitesimal displacements, or the finite-displacement /energy criterion/ proposed by tsien. In this paper the problem of the finite displacement and buckling of a shallow spherical dome is investigated both theoretically and experimentally. In the theoretical approach the nonlinear equations are converted into a sequence of linear equations by expanding all of the variables in powers of the center deflection and then equating the coefficients of equal powers. The basic parameter for the shallow dome is proportional to the ratio of the central height of the dome h to its thickness T. For small values of this ratio the expansions converge rapidly and enough terms are computed to determine the buckling load according to the classical criterion. For higher values of h t, convergence deteriorates rapidly and it was not possible to determine the buckling load with the number of terms which were computed. However even for these higher values of h t the deflection shapes are determined for deflection amplitudes below the amplitude at which buckling occurs. These deflection shapes are characterized by their rapid change as h t increases and by the fact that, over most of the range of h t studied, the maximum deflection does not occur at the center of the dome. Experimental results seem to indicate that the classical criterion of buckling is applicable to very shallow spherical domes for which the theoretical calculation was made. A transition to energy criterion for higher domes is also indicated.","title":"A nonlinear theory of bending and buckling of thin elastic shallow spherical shells.","url":"cran.html#doc827"},
{"title":"Symmetric joukowsky airfoils in shear flow.","url":"cran.html#doc452","description":"Tsien, H.S. Q. App. Math. 1, 1943, 130. The velocity components of the fluid far from the airfoil are given by where c is the chord of the airfoil, and k are constants, u and v are velocity components in the directions of the coordinates x and Y. The solution is sought in the form of the stream function and satisfies laplace's equation. A general expression for for vanishing disturbance velocities at points far from the origin is written, and the flows due to a source, a vortex and a solid circular cylinder in shear flow are considered as examples. Typical streamline patterns are shown for these cases. From the eulerian equations of motion the author obtains the expression for in terms of the parameter and derivatives of. The general form of is introduced and the appropriate solution for the pressure p is obtained. By integration around a contour enclosing the body, expressions are obtained, analogous to the blasius formulae, for the force and couple on any cylinder in this type of flow. These formulae are applied to the case of a symmetrical joukowsky airfoil. The method of conformal transformation is employed in the determination of. The boundary condition of tangential flow at the airfoil surface must be satisfied by the total flow in the airfoil plane, but this condition leads to a boundary condition for in the transformed plane. The kutta-joukowsky condition of finite velocity at the trailing edge also leads to a condition on in this plane. From these conditions and the general expression for the circulation and the strengths of the doublets and quadruplets required for the force and moment are determined. Hence, the formulae for lift and moment coefficient are obtained. These involve, in addition to the usual (potential-flow) terms, terms proportional to. The ten functions that appear in the expressions for the lift and moment coefficients are tabulated for values of the thickness ratio between 0 and 1. The aerodynamic-center position and the coefficient of the moment about the aerodynamic center are also calculated and are presented graphically as functions of."},
{"description":"Hanson, P.W. And Doggett, R.V. Nasa tn.d1391, 1962. 70 to 2. 87 and comparisons with theory. The aerodynamic damping of a flexibly mounted aeroelastic model with a blunted conical nose and a cylindrical afterbody was measured at mach numbers from 0.70 to 1.20 at several levels of dynamic pressure and two weight conditions and at mach numbers from 1.76 to 2.87 at one weight condition. The first two free-free flexible modes of vibration were investigated. Also investigated at mach numbers from 0.9 to 1.2 was the aerodynamic damping in the first free-free modes of a model which had a /hammerhead/ nose (the base diameter of the blunted cone was greater than the diameter of the afterbody which necessitated a reflex angle downstream from the cone base). Two basically different methods, the /electrical power-input/ and the /decaying oscillations/ methods were used to determine the damping and frequencies. The experimentally determined values are compared with some applicable theories. The results of the investigation indicate that the aerodynamic damping in the elastic modes of vibration was small for all configurations tested. The maximum aerodynamic damping measured in the first mode was on the order of damping. The aerodynamic damping was found to be even less for vibration modes higher than the first. Reduced-frequency effects were found to be negligible for the range investigated. Agreement of calculated aerodynamic damping derivatives with the experimental results was not good. Generally, the experimentally determined derivatives were larger than those predicted by the various theories used. The bond-packard theory appeared to give the best agreement for the first free-free vibration mode but gave the worst agreement for the second mode. Measurements made on the configuration that had a hammerhead nose indicated small negative aerodynamic damping in the mach number range from 0.95 to 1.00. Aerodynamic stiffness effects were found to be small and within the experimental scatter. (wind-on frequency determination was accurate only to approximately 1 percent.)","title":"Wind tunnel measurements of aerodynamic damping derivatives of a launch vehicle vibrating in free-free bending modes at mach numbers from 0. 70 to 2. 87 and comparisons with theory.","url":"cran.html#doc1066"},
{"url":"cran.html#doc717","title":"Motions of a short 10degree blunted cone entering a martian atmosphere at arbitrary angles of attack and arbitrary pitching rates.","description":"Peterson, V.L. Nasa tn-d 1326. The dynamic behavior of two probe vehicles entering a martian atmosphere in a passive manner with arbitrary initial angles of attack and pitching rates to 12degree per second has been determined. Results for an entry velocity of 21, 700 feet per second and an entry angle of -40degree were obtained from machine calculated solutions of the six-degree- of-freedom rigid-body equations of motion using experimental aerodynamic characteristics for the vehicles. One of the vehicles had a flat base and was statically stable in two attitudes /nose forward and base forward/. The other vehicle, derived from the first by adding a conical afterbody, was statically stable in only one attitude /nose forward/. A 10-rpm vehicle spin rate, believed ample for the purpose of distributing solar and aerodynamic heating over the vehicle surface, and model atmospheres encompassing the probable extremes for the planet were also considered. It was found that while the motion of the flat-based vehicle could be oscillatory about either the nose-forward or base-forward stable trim attitudes when aerodynamic heating rates were high, the range of initial angles of attack resulting in base-forward orientation was reduced by more than a factor of 3. When initial pitch rates were increased from body having only nose-forward stability showed that oscillatory angles of attack at maximum heating-rate conditions probably would not exceed about 25degrees although angles of attack when heating rates were 50 percent of maximum could be as high as 40degree. Values of these upper bound angles of attack were essentially independent of initial pitch rates for the range considered. Furthermore, the envelope of maximum probable angles of attack was increased only slightly when the vehicle was given a 10-rpm spin rate. The relationship between maximum amplitudes of oscillation and heating rates through high heating portions of the trajectories was preserved when model atmospheres believed to encompass the extreme possibilities for mars were used in the calculations"},
{"description":"Reissner, E. Naca tn.1832, 1949. A theory has been developed for small bending and stretching of sandwich-type shells. This theory is an extension of the known theory of homogeneous thin elastic shells. It was found that two effects are important in the present problem, which have not been considered previously in the theory of curved shells.. (1) the effect of transverse shear deformation and (2) the effect of transverse normal stress deformation. The first of these two effects has been known to be of importance in the theory of plates and beams. The second effect was found to occur in a manner which is typical for shells and has no counterpart in flat-plate theory. The general results of this report have been applied to the solution of problems concerning flat plates, circular rings, circular cylindrical shells, and spherical shells. In each case numerical examples have been given, illustrating the magnitude of the effects of transverse shear and normal stress deformation. The results of this investigation indicate the necessity of taking account of transverse shear and normal stress in sandwich-type shells, as soon as there is an order-of-magnitude difference between the elastic constants of the core layer and of the face layers of the composite shell. It was found that the changes due to transverse shear and normal stress deformation in the core may be so large as to be no mere corrections to the results of the theory without transverse core flexibility. The actual magnitude of the changes is greatly dependent on the geometry and loading condition of the structure under consideration so that no general rules may be given which indicate for which elastic modulus ratio the changes begin to be significant. Solutions of problems in the present theory may in general be obtained by mathematical methods which are similar to those employed in the theory of plates and shells without the effect of transverse shear and normal stress deformation included. The present work does not include consideration of buckling and finite deflection effects.","title":"Small bending and stretching of sandwich type shells.","url":"cran.html#doc826"},
{"title":"A comparative analysis of the performance of long range hypervelocity vehicles.","url":"cran.html#doc77","description":"Eggers, A.J. Naca tn.4046, 1957. Long-range hypervelocity vehicles are studied in terms of their motion in powered flight, and their motion and aerodynamic heating in unpowered flight. Powered flight is analyzed for an idealized propulsion system which rather closely approaches present-day rocket motors. Unpowered flight is characterized by a return to earth along a ballistic, skip, or glide trajectory. Only those trajectories are treated which yield the maximum range for a given velocity at the end of powered flight. Aerodynamic heating is treated in a manner similar to that employed previously by the senior authors in studying ballistic missiles (naca tn 4047), with the exception that radiant as well as convective heat transfer is considered in connection with glide and skip vehicles. The ballistic vehicle is found to be the least efficient of the several types studied in the sense that it generally requires the highest velocity at the end of powered flight in order to attain a given range. This disadvantage may be offset, however, by reducing convective heat transfer to the re-entry body through the artifice of increasing pressure drag in relation to friction drag - that is, by using a blunt body. Thus the kinetic energy required by the vehicle at the end of powered flight may be reduced by minimizing the mass of coolant material involved. The glide vehicle developing lift-drag ratios in the neighborhood of and greater than 4 is far superior to the ballistic vehicle in ability to convert velocity into range. It has the disadvantage of having far more heat convected to it,. However, it has the compensating advantage that this heat can in the main be radiated back to the atmosphere. Consequently, the mass of coolant material may be kept relatively low. The skip vehicle developing lift-drag ratios from about 1 to 4 is found to be superior to comparable ballistic and glide vehicles in converting velocity into range. At lift-drag ratios below 1 it is found to be about equal to comparable ballistic vehicles while at lift-drag ratios"},
{"description":"Watkins, C.E., woolston, D.S. And Cunningham, H.J.A. Nasa tr r-48, 1959. A detailed description is given of a method of approximating solutions to the integral equation that relates oscillatory or steady lift and downwash distributions on finite wings in subsonic flow. The method of solution is applicable to general plan forms with either curved or straight leading and trailing edges. Moreover, it is directly applicable to control surfaces such as all-movable tails but modifications are needed to apply it to controls in general. Applications of the method involve evaluations of numerous integrals that must be handled by numerical procedures but systematic schemes of evaluations have been adopted that are well suited to the routines of automatic digital computing machines. These schemes of evaluation have been incorporated in a program for an ibm 704 electronic data processing machine. With this machine, a pressure distribution together with such quantities as section or total lift and moment coefficients or generalized forces can be determined for a given value of frequency and mach number and for several /four or five/ modes of oscillation in about 4 minutes of machine time. In the case of steady downwash conditions corresponding quantities can be obtained in about 2 minutes of machine time. In order to illustrate applications of the method, results of several calculations are presented. In these illustrations total forces and moments are compared /1/ with results of analytic procedures for a circular plan form with steady downwash conditions, /2/ with results of other theories and with experiment for a rectangular plan form of aspect ratio 1 at a uniform angle of attack, and /3/ with some experimental results for a rectangular plan form of aspect ratio 2 undergoing pitching and flapping oscillations. Also included in the illustrations are results of flutter calculations compared with experimental results for an allmovable control surface of aspect ratio 3.50 and for a cantilevered rectangular plan form of aspect ratio 5.04.","url":"cran.html#doc704","title":"A systematic kernel function procedure for determining aerodynamic forces on oscillating or steady finite wings at subsonic speeds."},
{"description":"Whalen, R.J. J. Ae. Scs. 29, 1962, 1222. The condition of immediate freezing of the mass fraction of dissociated species of air at the equilibrium value behind the shock envelope prevails over a major portion of the flight spectrum associated with lifting re-entry vehicles. This is observed by means of order-of-magnitude considerations within the limits of the present knowledge of chemical reaction rates for the constituents of air. Accordingly, investigations of the viscous and inviscid hypersonic flow about blunt and sharp leading edge slender bodies are made. The investigations are generalized to consider an arbitrary degree of dissociation in the ambient free stream. This condition is included in order to allow comparison with the flow field about a model in the test section of a hypersonic facility with dissociated air species present in the free stream. Inviscid frozen flow investigations are made for blunt and sharp leading edge slender body power-law geometries. The results indicate that the influence of a finite leading edge, in inducing a pressure field far downstream (/blast-wave/ analogy), is considerably diminished for this model. This conclusion is verified numerically by a characteristics solution for the hypersonic flow about a /sonic-wedge/ slab. The viscous investigations consider the boundary-layer interaction problem with a frozen degree of dissociation. In this case, as in the inviscid analysis, the governing parameter is observed to be the ratio of the dissociation energy to the free-stream kinetic energy. The influence of this parameter on the boundary-layer interaction mechanism for a highly cooled, noncatalytic wall is presented. The influence of a frozen flow field on skin friction and heat transfer is also discussed. Finally, since higher mach number gas flows may be generated in wind tunnel nozzles where dissociation nonequilibrium effects are present, the possibility of employing expansions with a controlled degree of dissociation as a technique for aerodynamic simulation is presented.","title":"Viscous and inviscid nonequilibrium gas flows.","url":"cran.html#doc625"},
{"title":"Viscosity effects in sound waves of finite amplitude: in survey in mechanics.","url":"cran.html#doc132","description":"Lighthill, M.J. Ed. By G.K.batchelor and R.M.davies. C.U.P. 1956. This article has as its subject /the conflicting influence on sound propagation of convection on the one hand, and of diffusion and relaxation on the other/, whose importance in the determination of the structure of shock waves was first appreciated clearly by sir geoffrey taylor. As an essential introduction to the main topics, author gives an exceptionally clear and valuable account of the physical mechanisms of viscosity, thermal conductivity, and other diffusion effects, including relaxation. The classical theory of shock-wave formation is then discussed, and some extensions are made. The remainder of the article is based on the demonstration that the nonlinear equation for plane progressive sound waves, in which convection and diffusion are taken into account to a first approximation, can be transformed into burgers's equation, the general solution of which was given by hopf and cole. This approach, in which all flows are continuous (they become discontinuous at shock waves in the limit as viscosity, etc., tend to zero), allows the author to re-derive and extend whitham's theory of the formation and decay of weak plane shock waves, and to derive many new results, such as the velocity distributions during the union of two shock waves and during the formation of a shock wave. The application of the same idea to non-plane shock waves is also discussed, but more briefly,. In these cases, burgers's equation is not quite such a good approximation as before. The article concludes with sections on sound waves whose reynolds numbers based on the length scale of the flow and the velocity amplitude are comparable with unity, and on the effects of relaxation on the properties of shock waves. The whole is much more than a survey, and represents a very substantial advance in the theory of sound waves. It is the finest possible tribute to sir geoffrey taylor that he should be able to inspire articles such as this and the others in this volume."},
{"url":"cran.html#doc640","title":"The design of structures to resist jet noise fatigue.","description":"B. L. Clarkson J. Royal aero. Soc. 66, oct. 1962 The design of structures to resist jet noise fatigue demands a knowledge of a wide range of subjects from pure acoustics at one hand to metal physics at the other. At the present time the various aspects of the problem are not sufficiently well know quantitatively for a purely theoretical design study to be made. Never- the-less a knowledge of the behaviour of typical forms of construction in noise environments can be used with a limited amount of theoretical work to indicate tne most efficient types of structure. This approach to the problem is adopted in this lecture as it seems to be the most promising one available at the moment. It must be emphasized, however, that although some progress has been made in dicsovering the behaviour of a structure subjected to noise it is not possible to estimate the life of any component at the drawing board stage. Some prototype strain measurements and proof testing are therefore essential if one is to prove the integrity of the design. Within the structural limits of single skin construction set in this lecture the main conclusion to be reached is that no reasonable estimate of fatigue life can yet be made in the drawing board stage of a structure. Nevertheless, a study of the form of behaviour of typical structures has led to a theoretical simplification of the problem of skin vibration. From this it has been possible to suggest an optimum deisgn for a skin stiffened by stringers. A suggestion for an optimum design of skin and rib for control surfaces to minimise stresses at the rib-skin intersection is put forward but no experience can check this yet. The most resonable basis for the future estimation of fatigue life of a component appears to be the /random/ s-n curve and consierable effort should be made to obtain the necessary test data. The life expectation of a new design will be uncertain and some proof testing is essential if the integrity of structure in high noise levels (150 db) is to be guaranteed."},
{"url":"cran.html#doc73","title":"Investigation of the stability of the laminar boundary layer in a compressible fluid.","description":"Lees, L. And Lin, C.C. Naca tn.1115, 1946. In the present report the stability of two-dimensional laminar flows of a gas is investigated by the method of small perturbations. The chief emphasis is placed on the case of the laminar boundary layer. Part 1 of the present report deals with the general mathematical theory. The general equations governing one normal mode of the small velocity and temperature disturbances are derived and studied in great detail. It is found that for reynolds numbers of the order of those encountered in most aerodynamic problems, the temperature disturbances have only a negligible effect on those particular velocity solutions which depend primarily on the viscosity coefficient (/viscous solutions/). Indeed, the latter are actually of the same form in the compressible fluid as in the incompressible fluid, at least to the first approximation. Because of this fact, the mathematical analysis is greatly simplified. The final equation determining the characteristic values of the stability problem depends on the /inviscid solutions/ and the function of tietjens in a manner very similar to the case of the incompressible fluid. The second viscosity coefficient and the coefficient of heat conductivity do not enter the problem,. Only the ordinary coefficient of viscosity near the solid surface is involved. Part 2 deals with the limiting case of infinite reynolds numbers. The study of energy relations is very much emphasized. It is shown that the disturbance will gain energy from the main flow if the gradient of the product of mean density and mean vorticity near the solid surface has a sign opposite to that near the outer edge of the boundary layer. A general stability criterion has been obtained in terms of the gradient of the product of density and vorticity, analogous to the rayleigh-tollmien criterion for the case of an incompressible fluid. If this gradient vanishes for some value of the velocity ratio of the main flow exceeding 1-1/m (where m is the free stream mach number)."},
{"title":"A second order shock-expansion method applicable to bodies of revolution near zero lift.","url":"cran.html#doc234","description":"Syvertson, C.A. And Denis, D.H. Naca tn.3527. A second-order shock-expansion method applicable to bodies of revolution near zero lift is developed. Expressions defining the pressures on noninclined bodies are derived by the use of characteristics theory in combination with properties of the flow predicted by the generalized shock-expansion method. This result is extended to inclined bodies to obtain expressions for the normal-force and pitching-moment derivatives at zero angle of attack. The method is intended for application under conditions between the ranges of applicability of the second-order potential theory and the generalized shock-expansion mehtod - namely, when the ratio of free-stream mach number to nose fineness ratio is in the neighborhood of 1. For noninclined bodies, the pressure distributions predicted by the second-order shock-expansion method are compared with existing experimental results and with predictions of other theories. For inclined bodies, the normal-force derivatives and locations of the center of pressure at zero angle of attack predicted by the method are compared with experimental results for mach numbers from 3.00 to 6.28. Fineness ratio 7, 5, and 3 cones and tangent ogives were tested alone and with cylindrical afterbodies up to 10 diameters long. In general, the predictions of the present method are found to be in good agreement with the experimental results. For non-inclined bodies, pressure distributions predicted with the method are in good agreement with existing experimental results and with distributions obtained with the method of characteristics. For inclined bodies, the normal-force derivatives per radian (for normal-force coefficients referenced to body base area) are predicted within 0.2 and the locations of the center of pressure are predicted within 0.2 body diameters. On the basis of these results, the second-order shock-expansion method appears applicable for values of the ratio of free-stream mach number to nose fineness ratio from 0.4 to 2."},
{"title":"The calculation of transient temperature in turbine blades and tapered discs using biot's variational method.","url":"cran.html#doc869","description":"Howe, P.W.H. Arc cp.617, 1961. Transient temperatures in aerofoil sections and tapered discs are calculated taking advantage of simplifications in heat flow analysis achieved in biot's variational method. Cross-sections are represented by a line of adjacent squares of various sizes suitable for the local dimensions, E.G. Small squares near the leading and trailing edges. The potential, dissipation and surface dissipation functions of biot's method are set up, and the lagrange equations lead, by automatic procedures, to an eigenvalue formulation in matrix form for the temperatures and their first time derivatives. Solutions are sums of exponentials in time, and are evaluated by digital computer, requiring about five minutes for each cross-section and heat transfer coefficient. Transient temperatures in a particular aerofoil section for variation of heat transfer coefficient and for external temperature depending exponentially on time agree with results obtained on an analogue computer. Maximum transient temperature differences are evaluated for tapered discs by a simple electrical analogue) with variation of edge radius and heat transfer coefficient. Peculiarities in the solution for cyclic temperature external to an aerofoil over a range of frequencies indicate limitations in the mathematical formulation. A successful solution for cyclic external temperature might enable eigenvalues to be separated out in experimental measurements using electronic equipment, and this might be extended to exponential external temperature if a relationship between cyclic and exponential external temperature could be established. Eigenvalues and eigenvectors as discrete values arise fictitiously from the sub-division into squares and the possibility of an integral formulation is mentioned. There is a possible, but not immediate, extension to cooled blades, whose cross-sections are multiply-connected regions. Transient stresses due to creep, and viscoelasticity might be included."},
{"url":"cran.html#doc695","title":"Some experiments relating to the problem of simulation of hot jet engines in studies of jet effects on adjacent surfaces at a free-stream mach number of 1.80.","description":"Bressette, W.E. Naca rm l56e07. 1956. 80. An investigation at a free-stream mach number of 1.80 in a blowdown type tunnel was made to study the effect on the pressure distribution of a zero angle of attack wing surface when certain exhaust parameters of a hot turbojet engine are varied. Static-pressure surveys were made on a wing surface that was located in the vicinity of a small-scale propulsive jet. This propulsive jet was operated with four types of jet exhausts. These jet exhausts were a hot jet /hydrogen burned in air/, a cold air jet, a cold helium jet, and a jet composed of a mixture of two cold gases /hydrogen and carbon dioxide/. The hot jet, because of its high exhaust temperature /3, 300degreer/ and because combustion was performed in air, was believed reasonably able to simulate the exhaust parameters of an actual afterburning turbojet engine. The cold jets used were selected in order that the effects of a variation in the exhaust parameters of jet-exit static-pressure ratio, ratio of specific heats, density, and velocity, could be obtained by comparing each cold jet with the hot jet or with another cold jet. The tests were made over a range of jet-exit staticpressure ratios from 1 to 9 with values of the ratio of specific heats of 1.27, 1.40, and 1.66 and at variations in density and velocity of the order of approximately 8 and 3 times, respectively. Within the scope of this investigation, it was found that jet-exit static-pressure ratio and the ratio of specific heats affected the pressure distribution on the wing associated with jet interference while a variation in exit velocity and density did not. The jet-exit staticpressure ratio affected the wing pressure distribution in a major way while the ratio of specific heats had only a minor effect. The addition of temperature in the propulsive jet exhaust at a jet-exit staticpressure ratio of 4 had little or no effect on the pressure distribution associated with jet interference on the wing."},
{"title":"Propeller in yaw.","url":"cran.html#doc210","description":"Ribner, H.S. Naca r820, 1945. It was realized as early as 1909 that a propeller in yaw develops a side force like that of a fin. In 1917, R. G. Harris expressed this force in terms of the torque coefficient for the unyawed propeller. Of several attempts to express the side force directly in terms of the shape of the blades, however, none has been completely satisfactory. An analysis that incorporates induction effects not adequately covered in previous work and that gives good agreement with experiment over a wide range of operating conditions is presented herein. The present analysis shows that the fin analogy may be extended to the form of the side-force expression and that the effective fin area may be taken as the projected side area of the propeller. The effective aspect ratio is of the order of 8 and the appropriate dynamic pressure is roughly that at the propeller disk as augmented by the inflow. The variation of the inflow velocity, for a fixed-pitch propeller, accounts for most of the variation of side force with advance-diameter ratio v nd. The propeller forces due to an angular velocity of pitch are also analyzed and are shown to be very small for the pitching velocities that may actually be realized in maneuvers, with the exception of the spin. Further conclusions are.. A dual-rotating propeller in yaw develops up to one-third more side force than a single-rotating propeller. A yawed single-rotating propeller experiences a pitching moment in addition to the side force. The pitching moment is of the order of the moment produced by a force equal to the side force, acting at the end of a lever arm equal to the propeller radius. This cross-coupling between pitch and yaw is small but possibly not negligible. The formulas for propellers in yaw derived herein (with the exception of the compressibility correction) and a series of charts of the side-force derivative calculated therefrom have been presented without derivation in an earlier report."},
{"title":"The generalized expansion method and its application to bodies travelling at high supersonic airspeeds.","url":"cran.html#doc373","description":"Eggers, A.J., savin, R.C. And Syvertson, C.A. J.ae.scs. 22, 1955, 231. It is demonstrated that the shock-expansion method can be generalized to treat a large class of hypersonic flows, only one of which is flow about airfoils. This generalized method predicts the whole flow field, including shock-wave curvatures and resulting vorticity, providing that (1) disturbances originating on the surface of an object are largely absorbed in shock waves with which they interact and (2) disturbances associated with the divergence of stream lines in tangent planes to the surface are of secondary importance compared to those associated with the curvature of stream lines in planes normal to the surface. It is shown that these conditions may be met in three-dimensional as well as two-dimensional hypersonic flows. When they are met, surface streamlines may be taken as geodesics, which, in turn, may be related to the geometry of the surface. The validity of the generalized shock-expansion method for three-dimensional hypersonic flows is checked by comparing predictions of theory with experiment for the surface pressures and bow shock waves of bodies of revolution. The bodies treated are two ogives having fineness ratios of 3 and 5. Tests were conducted at mach numbers from 2.7 to 6.3 and angles of attack up to 15 degrees in the 10- by 14-in. Supersonic wind tunnel of the ames aeronautical laboratory. At the lower angles of attack, theory and experiment approach agreement when the ratio of mach number to fineness ratio--that is, the hypersonic similarity parameter--exceeds 1. At the larger angles of attack, theory tends to break down, as would be expected, on the leeward sides of the bodies. As a final point, it is inquired if the two-dimensionality of inviscid hypersonic flows has any counterpart in hypersonic boundary-layer flows. The question is answered in the affirmative, and results of experiment are employed to provide a partial check of this conclusion."},
{"description":"Gdalia kleinstein Polytechnic institute of brooklyn An extension of the modified-oseen method of carrier, based on the linearization of the viscous term of the von mises transformation, is presented. The method is employed to determine the velocity field associated with the laminar axisymmetric jet flow of a compressible gas with an arbitrary but constant external flow. The approximate solution is shown to be in good agreement with the exact numerical calculation of pai. In many boundary layer problems it is not possible to make the assumption of flow similarity. The solution in these cases can be obtained either by laborious finite difference techniques or by resort to approximate solutions. Carrier and lewis (1), and more recently carrier (2), have suggested a method of obtaining approximate solutions to problems involving convection and diffusion. This method, termed by carrier /the modified-oseen method/, overcomes an essential difficulty of integral methods, namely, the generation of reasonable profiles. It is well known that the integral method gives accurate results only if the analytical profiles represent closely the true profiles. According to the modified-oseen method the convective operator in the original partial differential equation is replaced by a linear one. The resulting equation for the boundary layer problem is the heat conduction equation which can be treated by well-known techniques. It is the purpose of this paper to indicate a modification of this procedure and to demonstrate its simplicity and accuracy by treating the axisymmetric laminar flow of a compressible gas with arbitrary but constant external flow. The modification is based on the use of the von mises transformation with a subsequent linearization of the viscous term, rather than the linearization of the convective term. Pai's problem (3), originally treated by a finite difference technique, is considered to illustrate the effectiveness of this method.","title":"An approximate solution for the axisymmetric jet of a laminar compressible fluid.","url":"cran.html#doc1375"},
{"description":"Williams, J. Arc r + m 2492, 1951. The term flutter is used here to denote maintained or violent oscillations of a structure due to aerodynamic forces acting in conjunction with both elastic and inertial forces. Attention is restricted to this particular branch of the more general field of aeroelasticity, which embraces buffeting, divergence, and reversal of control, as well as flutter,. Airscrew flutter is not specifically considered. The monograph is divided into three main parts, each of which has been made self-contained for the convenience of readers. In the first part, general methods for the investigation of aircraft flutter, by theoretical analysis and by experiments on flutter models, are set out and discussed. A detailed account of the aerodynamic theory of wings in non-uniform motion is not included, since this has already been provided elsewhere, but methods for the evaluation of the aerodynamic forces required in a theoretical flutter analysis are logically developed, and a bibliography of researches on the aerodynamic theory is given in the appendix. Investigations on specific types of aircraft flutter--namely wing flutter, control surface flutter, and tab flutter--are discussed in part these various types of flutter are considered, but the practical details of flutter-prevention devices are omitted. Finally, in part 3, methods for the experimental determination of airloads on oscillating aerofoil systems are described, and available airload measurements are analysed and compared with theoretical results. An attempt has been made to refer in the text to all relevant british work reported by the early part of 1947. Foreign work has been mentioned in parts 1 and 2 only where necessary for the sake of completeness, but in part 3 and the appendix all relevant foreign references known to the author have been included. Matrix notation has been used for the theoretical treatment in part 1, but otherwise its use has been avoided.","url":"cran.html#doc202","title":"Aircraft flutter."},
{"description":"Von karman, T. And Tsien, H.S. J. Ae. Scs. 8, 1941, 303. In two previous papers the authors have discussed in detail the inadequacy of the classical theory of thin shells in explaining the buckling phenomenon of cylindrical and spherical shells. It was shown that not only the calculated buckling load is 3 to 5 times higher than that found by experiments, but the observed wave pattern of the buckled shell is also different from that predicted. Furthermore, it was pointed out that the different explanations for this discrepancy advanced by L. H. Donnell and W. Flugge are untenable when certain conclusions drawn from these explanations are compared with the experimental facts. By a theoretical investigation on spherical shells the authors were led to the belief that in general the buckling phenomenon of curved shells can only be explained by means of a non-linear large deflection theory. This point of view was substantiated by model experiments on slender columns with non-linear elastic support. The non-linear characteristics of such structures cause the load necessary to keep the shell in equilibrium to drop very rapidly with increase in wave amplitude once the structure started to buckle. Thus, first of all, a part of the elastic energy stored in the shell is released once the buckling has started,. This explains the observed rapidity of the buckling process. Furthermore, as it was shown in one of the previous papers the buckling load itself can be materially reduced by slight imperfections in the test specimen and vibrations during the testing process. In this paper, the same ideas are applied to the case of a thin uniform cylindrical shell under axial compression. First it is shown by an approximate calculation that again the load sustained by the shell drops with increasing deflection. Then the results of this calculation are used for a more detailed discussion of the buckling process as observed in an actual testing machine.","title":"The buckling of thin cylindrical shells under axial compression.","url":"cran.html#doc739"},
{"description":"Naca rm e56b03b, 1956. Chapter xiii An analysis of the part-speed operating problems of high-pressure-ratio ratio multistage axial-flow compressors was made by means of a simplified stage-stacking study. The principal problems considered were poor low-speed efficiency, multiple-valued performance characteristics at intermediate speeds, and poor intermediate-speed compressor surge or stall-limit characteristics. The analysis indicated that all these problems could be attributed to discontinuities in the performance characteristics of the front stages. Such discontinuities can be due to the type of stage stall or to a deterioration of stage performance resulting from stall of adjacent stages. The effects of compromises of stage matching to favor part-speed operation were also considered. This phase of the study indicated that such compromises would severly reduce the complete-compressor-stall margin. Furthermore, the low-speed stage stall problem is transferred from the inlet stages to the middle stages, which are more susceptible to abrupt-stall characteristics. The analysis indicates that inlet stages having continuous performance characteristics at their stall points are desirable with respect to part-speed compressor performance. These characteristics must, however, be obtained when the stages are operating in the flow environment of the multistage compressor. Alleviation of part-speed operation problems may also be obtained by improvement in either stage flow range or stage- loading margin. The results of this analysis are only qualitative. The trends obtained, however, are in agreement with those obtained from experimental studies of high-pressure-ratio multistage axial-flow compressors, and the results are valuable in developing an understanding of the off-design problem. In addition to these stage-matching studies, a general discussion of variable-geometry features such as air bleed and adjustable blades is included.","url":"cran.html#doc588","title":"Compressor operation with one or more blade rows stalled."},
{"description":"Ordway, D.E. And Hale, R.W. J. Ae. Scs. 1960, 437. A supersonic propeller with blades attached to an infinite cylinder as a hub is studied. The forward speed may be subsonic, but the relative speed at each section is supersonic. The lightly loaded blades are represented by a surface distribution of appropriate /modified/ sources in a fashion similar to ordinary supersonic thin-wing theory. These sources are found by approximating the exact potential for a constant-strength compressible source traveling along a helical path. The usual relationship between the source strength and boundary condition is found,. And Subsequently the source distribution is given, to the appropriate order, in terms of the blade geometry. Tip effects are considered by extending the theory of evvard and krasilshchikova. The present investigation, however, is restricted to those planforms for which no vortex sheet appears off the tip. For points in the tip region, the potential is obtained through the appropriate distribution of /modified/ sources in the upwash region off the tip. By transforming to a curvilinear, nonorthogonal coordinate system coincident with the modified mach lines described by the infinities of the potential, an integral equation for the required source distribution in the upwash region is derived. Without having to solve this equation, it is shown that the potential for a point in the tip region can be obtained in terms of an integration of known source distributions over the blade surface only. The case of a twisted flat plate of particular planform is treated, and a sample calculation is made of the pressure distribution at selected radial positions within the noncommunicating portion of the blade, as well as over the entire tip region. Though this analysis is carried out explicitly for the supersonic propeller, it could also be extended to calculate various rotary derivatives for highspeed flight vehicles.","title":"Theory of supersonic propeller aerodynamics.","url":"cran.html#doc1271"},
{"description":"Rogers, E.w E., townsend, J.E.G. And Berry, C.J. A.R.C., r + m 3270, may 1960. Summary. An investigation has been made in the N.P.L. 18 in. X 14 in. Tunnel of the effects of leading-edge modifications on the flow and forces on an untapered wing of 50 deg leading-edge sweep, at stream mach numbers between 0 60 and 1 20. Seven leading-edge profiles were tested, ranging from a drooped extension of 18 per cent of the chord of the basic sharp-nosed section to a round-nosed section with a leading-edge radius of 1 0 per cent of the basic chord. Leading-edge droop was found to increase the wing drag near zero lift but to reduce appreciably the lift-dependent drag component, except at the highest test mach numbers. Droop also increased the lift coefficient at which leading-edge separation occurred on the upper surface at moderate subsonic speeds, but in addition reduced the mach number for transonic flow attachment. The appearance of the forward shock /but not the rear shock/ is considerably delayed when the leading edge is drooped. With the undrooped sections an increase in leading-edge radius was accompanied by successively earlier appearances of the forward shock, and hence the outboard shock with its attendant separation. The conditions at which the rear shock first appeared changed only slowly as the section was changed. The variations in wing flow pattern as the leading edge is modified are discussed and related to measured changes in the wing lift and drag. An attempt is also made to estimate the local mach numbers on some parts of the wing from the oil-flow patterns,. This material is used to assess the flow conditions appropriate to shock-induced separation. The main section of the report concludes with a tentative discussion of the significance of the present results to the design of swept wings. In an appendix results obtained with the wing in a sweptforward configuration are briefly considered.","title":"A study of the effect of leading-edge modifications on the flow over a 50degree sweptback wing at transonic speeds.","url":"cran.html#doc797"},
{"url":"cran.html#doc712","title":"Low-speed longitudinal aerodynamic characteristics associated with a series of low-aspect ratio wings having variations in leading-edge contour.","description":"Spencer, B. And Hammond, A.D. Nasa tn d-1374, 1962. An investigation has been conducted at various reynolds numbers and low subsonic speeds to determine the longitudinal aerodynamic characteristics associated with a series of low-aspect-ratio wings having variations in leading-edge contours. The planforms included a highly swept triangular wing, a rectangular wing, and intermediate wings including planforms having elliptic and parabolic leading-edge contours, all having an aspect ratio of 1.33. The effects of changing aspect ratio for a given leading-edge contour were investigated for two of the wings presented,. Also included are the longitudinal characteristics associated with various fuselage sizes. An effort has been made to estimate the lift variation with angle of attack for the wing planforms of the present investigation. Improvements in the lifting capabilities at low subsonic speeds associated with a basic triangular planform of low aspect ratio are possible by slight alterations in leading-edge design, which should still conform to possible design requirements at hypersonic speeds. These changes in planform resulted in increases in lift-curve slope, lift at high angles of attack, and in the maximum untrimmed lift-drag ratio, provided the fuselage was sufficiently small. The longitudinal stability characteristics of the majority of planforms indicate more desirable stability characteristics at high lifts than either a triangular wing or rectangular wing of the same aspect ratio. The effects of increasing reynolds number for each of the planforms investigated generally resulted in slight reductions in the lift at high angles of attack. A method is presented for estimating the subsonic-lift variation with angle of attack for the low-aspect-ratio wings of the present investigation and indicated good agreement with experimental data throughout the angle-of-attack range of this investigation."},
{"title":"The fundamentals of the statistical theory of turbulence.","url":"cran.html#doc99","description":"Th. Von karman California institute of technology Statistical theory in general considers mean values of certain quantities. In the case of the turbulent motion one is interested in mean values of velocities and of their derivatives, and in mean values of squares and products of velocities and their derivatives. It was O. Reynolds who first expressed the so-called apparent or turbulent stresses by the mean values of the products of the velocity components. The different theories suggested so far have as their common objective the establishment of relations between certain mean values, E.G. Between the turbulent shear stresses given by the mean products of velocity fluctuations and the derivatives of the mean velocities, I.E. The measured mean velocity gradients. In this sort of investigations the conception of the /correlation/ is of paramount importance. The late A. Friedman tried to introduce the correlations as unknown variables in the hydrodynamic equations., however, he could not carry his investigations to practical results, I.E., to results which can be compared with the experimental evidence. Recently, G. I. Taylor had success in his analysis of /isotropic/ turbulence by means of correlation calculations, and was able to discuss, theoretically, the problem of the decay of turbulence in a windstream behind a turbulence producing device. His theory raised considerable interest because it is concerned with the important problem of wind-tunnel turbulence and its results could be compared directly with experimental work done by dryden in this country and by fage, townend and simmons in england. The present paper is concerned with two fundamental problems.. With uniform isotropic turbulence and with the turbulent friction in a parallel stream. First, the general theory of isotropic turbulence is developed. This general theory includes taylor's consideration as a special case. However, it"},
{"description":"Chapman, D.R. Nasa r-11, 1959. The pair of motion equations for entry into a planetary atmosphere is reduced to a single, ordinary, nonlinear differential equation of second order by disregarding two relatively small terms and by introduring a certain mathematical transformation. The reduced equation includes various terms, certain of which represent the gravity force, the centrifugal acceleration, and the lift force. If these particular terms are disregarded, the differential equation is linear and yields precisely the solution of allen and eggers applicable to ballistic entry at relatively steep angles of descent. If all the other terms in the basic equation are disregarded (corresponding to negligible vertical acceleration and negligible vertical component of drag force), the resulting truncated differential equation yields the solution of sanger for equilibrium flight of glide vehicles with relatively large lift-drag ratios. A number of solutions for lifting and nonlifting vehicles entering at various initial angles also have been obtained from the complete nonlinear equation. These solutions are universal in the sense that a single solution determines the motion and heating of a vehicle of arbitrary weight, dimensions, and shape entering an arbitrary planetary atmosphere. One solution is required for each lift-drag ratio. These solutions are used to study the deceleration, heating rate, and total heat absorbed for entry into venus, earth, mars, and jupiter. From the equations developed for heating rates, and from available information on human tolerance limits to acceleration stress, approximate conditions for minimizing the aerodynamic heating of a trimmed vehicle with constant lift-drag ratio are established for several types of manned entry. A brief study is included of the process of atmosphere braking for slowing a vehicle from near escape velocity to near satellite velocity.","title":"An approximate analytical method for studying entry into planetary atmospheres.","url":"cran.html#doc164"},
{"title":"Experiments on the use of suction through perforated strips for maintaining laminar flow. Transition and drag measurements.","url":"cran.html#doc1325","description":"Gregory, N. And Walker, W.S. Arc r + m 3083, 1955. Transition and drag measurements. Wind-tunnel tests are described in which suction is applied at perforated strips, as an alternative to porous strips or slots, in order to maintain a laminar boundary layer. A test was first carried out on a single row of perforations on a cambered plate, as a preliminary to the main tests which were performed on strips of multiple rows of perforations drilled through the surface of a low-drag-type aerofoil 13 per cent thick and of 5-ft chord. Up to a wind speed of 180 ft sec it has been ascertained that suction may be safely applied to extend laminar flow provided the ratio of hole diameter to boundary-layer displacement thickness is less than 2, the ratio of hole pitch to diameter is less than 3 and there are at least three rows of holes in the strip. With less than three rows, the criteria are much more restrictive. It is possible to extend laminar flow by suction through perforations whose diameters and pitches exceed these values slightly, but only with the risk that excessive suction quantities will produce wedges of turbulent boundary layer originating at the holes. A uniform distribution of suction through the holes was necessary. This was successfully obtained by two methods, the use of cells and throttle holes, and with tapered holes. In particular, tests were carried out on some panels supplied by handley page, ltd., in which the cells and tapered holes had been constructed by commercial methods, and the suction distribution proved satisfactory. The resistance of some of the cellular arrangements was measured. It was found that when the suction quantities were the minimum required to maintain laminar flow, the additional losses in total head of the sucked air due to the resistance of the throttle holes could be made small compared with the loss in total head of the sucked boundary layer."},
{"description":"Wallace, J. And Clarke, J.H. Aiaa jnl. 1, 1963, 179. Considered is the second-order supersonic flow over a cruciform configuration consisting of two intersecting rectangular wings of high aspect ratio. The practical interest is in application to supersonic inlets, wing-body junctions and vehicle fins. The fundamental interest centers about identification and adjustment of the severe local failures of the ordinary second-order theory. For wings with discontinuous slopes, discontinuous potentials occur across the planar shock and square-root singularities in the velocities occur at the intersection of these shocks with the cruciform surfaces. The problem is simple enough so that these interesting features stand out clearly. A second-order solution uniformly valid to first order is constructed by adjustment of the ordinary second-order solution obtained first. The uniformly valid solution has two different series representations in the thickness parameter. One is the ordinary second-order series in ascending integral powers of the thickness parameter which is valid in the interior of the vertex-centered undisturbed mach cone, and the other is a series containing fractional powers which is valid adjacent to and upstream of this mach cone. The uniformly valid solution gives the detailed wave structure and shows a flow regime upstream of the vertex-centered undisturbed mach cone not predicted by the ordinary theory. The two solutions are otherwise identical. The wave structure consists of a pyramidal arrangement of planar shocks adjacent to and upstream of the above cone, followed by weaker oblique expansion fans and finally by two extremely weak shocks coincident with the vertex-centered undisturbed mach cone. As an example of the above, detailed results are presented for the case of two intersecting wedges. Application of the techniques to other quasi-cylindrical problems is discussed.","title":"Uniformly valid second-order solution for supersonic flow over cruciform surfaces.","url":"cran.html#doc1202"},
{"description":"William A. Newsom, jr., and louis P. Tosti Technical note d-1382 A collection of data from a number of brief investigations made with three different models to determine the character of the slipstream flow along the ground is presented for multiple-propeller tilt-wing vtol aircraft configurations operating near the ground. In general, the tests involved tuft surveys and slipstream dynamic-pressure measurements for several tilt-wing vtol models. A more extensive series of tests, including some measurements of the erosion of gravel by the slipstream and some measurements of the unsteady rolling, yawing, and pitching moments, was also made on one of the models operating in the hovering condition near the ground. The results of the flow studies indicated the presence of a stronger and deeper slipstream flow along the center line of the aircraft, and to some extent along parallel planes between adjacent propellers (on one wing), than to the side of the aircraft. This effect is caused by an intensification of the individual slipstreams as they meet at the planes of flow symmetry. The intensified flow along the center line of the aircraft is amplified by the presence of the fuselage and causes the dynamic pressure to be greater in front of the aircraft than would be expected on the basis of the slipstream of the individual propellers. In the erosion tests it was found that gravel, if sufficiently small, was rapidly eroded by the slipstream and that this gravel could be thrown high into the air if it struck even very small fixed obstacles on the ground (obstacles with a height less than the diameter of the gravel). Results of the investigation of moment fluctuations indicated that there are large, erratic variations of rolling, yawing, and pitching moments and that the propellers, reacting to an erratic inflow from the recirculating slipstream, are the primary source of these moments.","title":"Slipstream flow around several tilt-wing vtol aircraft models operating near the ground.","url":"cran.html#doc1144"},
{"description":"Green, L. And Nall, K.L. J. Ae. Scs. 1959, 689. App. Math. 7, 1950, 381. Experiments on porous-wall cooling and flow separation control in a supersonic nozzle. Control of flow separation by fluid injection at one diverging boundary of a two-dimensional, transparent-walled de laval nozzle was investigated by spark schlieren photography of dry nitrogen flows expanded from two stagnation temperatures injection conditions at the permeable boundary were varied by the use of three grades of porous stainless steel with nominal pore diameters of 10, 20, and 30 microns, through which nitrogen was forced by coolant reservoir pressures of 25, 50, and 100 psig, in addition to the case of no forced injection. Pressure distribution measurements were made along the nonpermeable diverging boundary. It was found that flow separation at expansion ratios approaching the optimum value for maximum thrust coefficient could be induced at the porous wall by a local injection mass velocity of the order of a few per cent of the local main-stream mass velocity. Separation at the solid boundary was not noticeably influenced by injection at the opposite wall, and the asymmetrical separation thus effected jet deflections of up to 10 degrees at the lower stagnation-pressure levels. Variation of the wall heat-transfer condition by changing the stagnation temperature did not significantly influence separation behavior. Temperature measurements at the reservoir face of the porous section, together with use of published correlations and of the rube-sin analysis for estimation of stream-side stanton numbers under noninjection and injection conditions, respectively, permitted heat-transfer calculations which indicated that the effectiveness of the transpiration technique in controlling nozzle wall temperatures derives primarily from intimate fluid-solid contact in a porous material of high specific surface.","title":"Q. App. Math. 7, 1950, 381. Experiments on porous-wall cooling and flow separation control in a supersonic nozzle.","url":"cran.html#doc773"},
{"description":"Rogers, E.W.E., hall, I.M. And Berry, C.J. Arc r + M.3286, 1960. 8 and 1. 41. A study has been made of the flow development over the wing as the incidence and stream mach number vary and this is illustrated by surface pressure distributions and oil-flow patterns. The growth and movement of the two main surface shocks (the rear and forward shocks) is discussed, and conditions for flow separation through these shocks are considered. For the rear shock, which has little sweep, these conditions are similar to those for shock-induced separation on two-dimensional aerofoils. The forward shock is comparatively highly swept and separation seems to correspond to two rather different but simultaneously-attained conditions, one related to the component mach number normal to the shock front and the other to the position of the reattachment line. The flow in the region between the leading edge and the forward shock is shown to have certain characteristics analogous to those found upstream of the shock on two-dimensional aerofoils. To the rear of the forward shock, but ahead of the rear shock, the flow at low supersonic speeds resembles in some respects that about a simple cone. The general flow development is related in the text to the wing lift and pitching moment, and the drag. The first two are most affected by the aft movement of the rear shock, which also stimulates the transonic drag rise. The lift-dependent drag is shown to be influenced by the appearance of leading-edge separation and possibly also by some stage in the development of the forward shock. The flow over the cropped-delta planform is noteworthy for the absence of the strong outboard shock and this is attributed partly to the cropped tip and partly to the unswept trailing edge. A comparison is made with results obtained during preliminary tests in which the wing planform closely resembled that of a true delta.","title":"An investigation of the flow about a plane half-wing of cropped delta planform and 6( symmetrical section at stream mach numbers between 0. 8 and 1. 41.","url":"cran.html#doc757"},
{"description":"Adams, E.W. Nasa tn.d564, 1961. The melting-type heat protection at the stagnation point of a re-entering irbm is treated by employing homogeneous, opaque, and nondecomposing glass shields which do not exceed a temperature of some effects due to variations of the glass properties. The ballistic re-entry vehicle has a nose diameter of 0.635 m, a ballistic factor of 3.5 x 10, a re-entry angle of 124.9 (from the vertical) at an altitude of 100 km, and a re-entry speed of 4.5. The performance of 36 different glass shields with assumed combinations of material properties is investigated by employing a calculation method which yields practically exact, transient solutions for the problem. As a corollary, results for a certain steady flight state are also given. The discussions made it possible to derive under realistic flight conditions some thermal characteristics for the employment of thin, or light-weight, glass shields. Investigation of these hypothetical glass shields leads to the conclusion that a low thermal conductivity and a high specific heat, and thus, a small thermal diffusivity are most desirable. A small thermal diffusivity yields high surface temperatures, causing a high radiative heat transfer out of the shield,. And Steep temperature profiles normal to the surface, causing a small thermal penetration across the shield with little total ablation of the shield. Results show that for the assumed irbm re-entry, the necessary thickness of the employed glass shields increases monotonically with thermal diffusivity which is the only material parameter affecting this thickness. A high viscosity level and a high emissivity constant of the surface of the supposedly opaque shield are also desirable,. Although, these two properties exert a comparatively small influence on the overall performance when disregarding glass shields with an extremely low viscosity level.","title":"Theoretical investigation of the ablation of a glass-type heat protection shield of varied material properties at the stagnation point of a re-entering irbm.","url":"cran.html#doc82"},
{"description":"Korkegi, R.H. J. Ae. Scs. 23, 1956, 97. 8. An investigation of transition and skin friction on an insulated flat plate, 5 by 26 in., was made in the galcit 5 by 5 in. Hypersonic wind tunnel at a nominal mach number of 5.8. The phosphorescent lacquer technique was used for transition detection and was found to be in good agreement with total-head rake measurements along the plate surface and pitot boundary- layer surveys. It was found that the boundary layer was laminar at reynolds numbers of at least 5 x 10. Transverse contamination caused by the turbulent boundary layer on the tunnel sidewall originated far downstream of the flat plate leading edge at reynolds numbers of 1.5 to 2 x 10, and spread at a uniform angle of 5 compared to 9 degree in low-speed flow. The effect of two-dimensional and local disturbances was investigated. The technique of air injection into the boundary layer as a means of hastening transition was extensively used. Although the onset of transition occurred at reynolds numbers as low as 10, a fully developed turbulent boundary layer was not obtained at reynolds numbers much below 2 x 10 regardless of the amount of air injected. A qualitative discussion of these results is given with emphasis on the possibility of a greater stability of the laminar boundary layer in hypersonic flow than at lower speeds. Direct skin-friction measurements were made by means of the floating element technique, over a range of reynolds numbers verified as being laminar over the complete range. With air injection, turbulent shear was obtained only for reynolds numbers greater than 2 x 10, this value being in good agreement with earlier results of this investigation. The turbulent skin-friction coefficient was found to be approximately 0.40 of that for incompressible flow for a constant value of r, and 0.46 for an effective reynolds number between 5 and 6 x 10.","url":"cran.html#doc9","title":"Transition studies and skin friction measurements on an insulated flat plate at a mach number of 5.8."},
{"description":"Anderson, K. And Sinchtel, C.D. Nasa tn.d671, 1961. As a result of studies made during the international geophysical year (igy) and the international geophysical cooperation (igc), it is known that a considerable fraction of large solar flares give rise to almost pure streams of protons which reach the earth and continue to arrive for as long as 11 days. The energies of these particles lie within a very steep spectrum extending from 20 to least 500 mev. Because of the frequency of large flares during times of high solar activity, and owing to the long duration of each solar proton emission, these particles were present in detectable intensity near the top of the earth's atmosphere for about 15 percent of the time from 1957 to 1960. The number of large flares that accelerated and released these particles during this three-year period was about 30. The event that began on august 22, 1958 contributed greatly toward the understanding of the solar and terrestrial sequence of events, and in addition provided the first identification of the emitted particles. A flare on may of protons in the neighborhood of the earth that this phenomenon was recognized as an additional radiation hazard to manned vehicles in the high atmosphere and in most parts of the solar system. The three very intense events that occurred in july, 1959 further supported this conclusion, and the possibility of predicting such events became an important consideration. In addition to its value in the protection of human beings, effective forecasting clearly would be of great value in the detailed scientific study of this phenomenon. This paper presents a preliminary discussion of some aspects of predicting the arrival of protons at the earth following the appearance of solar activity features and, equally important, of forecasting the periods when this penetrating radiation is unlikely to occur.","url":"cran.html#doc83","title":"Discussion of solar proton events and manned space flights."},
{"description":"Hartree, D.R. Arc r + M.2427, 1949. The solution of the equations of the laminar boundary layer has been carried out for the pressure distribution for an elliptic cylinder of axial ratio 2.96.. 1 with its major axis in the direction of the incident stream. The solution has been obtained by the method of hartree and womersley. In applying this method the derivatives parallel to the boundary are replaced by finite differences, so that the partial differential equation of the boundary layer is replaced by an ordinary equation relating the velocity distribution through the boundary layer at one section to that at another, at an interval upstream. By two independent integrations covering the same range by finite intervals of different sizes, it is possible to estimate the errors involved in replacing the derivatives by finite differences, and so to correct for these errors. The process of solution requires the values of the pressure gradient along the solid boundary, and there is a certain tolerance in the derivation of the pressure gradient distribution from a limited number of observed values of pressure. An analysis of schubauer's pressure distribution is outlined, and the results were used for the main solution calculated. It is found that the solution, for the distribution of pressure gradient so derived, does not give separation of the boundary layer from the solid boundary, whereas the actual flow does separate. It is found that the calculated solution is very sensitive to the pressure distribution, and a comparatively small modification of the pressure distribution gives a solution which does indicate separation close to the point at which separation is observed to occur. The solution with this pressure distribution also gives very good agreement with the observed velocity distribution through the boundary layer at points upstream from separation.","title":"The solution of the equations of the laminar boundary layer for schubauer's observed pressure distribution for an elliptic cylinder.","url":"cran.html#doc1382"},
{"description":"Dean R. Chapman A study is made of the advantages that can be realized in compressible-flow research by employing a substitute heavy gas in place of air. Most heavy gases considered in previous investigations are either toxic, chemically active, or (as in the case of the freons) have a ratio of specific heats greatly different from air. The present report is based on the idea that by properly mixing a heavy monatomic gas with a suitable heavy polyatomic gas, it is possible to obtain a heavy gas mixture which has the correct ratio of specific heats and which is nontoxic, nonflammable, thermally stable, chemically inert, and comprised of commercially available components. Calculations were made of wind-tunnel characteristics for 63 gas pairs comprising 21 different polyatomic gases properly mixed with each of three monatomic gases (argon, krypton, and xenon). For a given mach number, reynolds number, and tunnel pressure, a gas-mixture wind tunnel having the same specific-heat ratio as air would be appreciably smaller and would require much less power than a corresponding air wind tunnel. Analogous though different advantages can be realized in compressor research and in firing-range research. The most significant applications, perhaps, arise through selecting and proportioning a gas mixture so as to have at ordinary wind-tunnel temperatures certain dimensionless characteristics which air at flight temperatures possesses but which air at ordinary wind-tunnel temperatures does not possess. Characteristics which involve the relaxation time (or bulk viscosity), the variation of viscosity with temperature, and the variation of specific heat with temperature fall within this category. Other applications arise in heat-transfer research since certain gas mixtures can be concocted to have any prandtl number in the range at least between 0.2 and 0.8.","url":"cran.html#doc185","title":"Some possibilities of using gas mixtures other than in aerodynamic research."},
{"url":"cran.html#doc946","title":"Exploratory investigation of the effect of a forward facing jet on the bow shock of a blunt body in a mach number 6 free stream.","description":"Romeo, D.J. And Sterrett, J.R. Nasa tn.d1605, 1963. The effect of a forward-facing jet on the bow shock of a blunt body in a mach 6 free stream was investigated experimentally. The models tested had forward-facing jets using air and helium exhausting at mach numbers from 1 to 10.3 and were run through a range of the ratio of jet total pressure to free-stream total pressure of 0.03 (jet off) to 2.5. The ratio of body diameter to jet-exit diameter varied from 1.12 to 55.6 and the angle of attack was varied from 0 to 35. The experimental results show that the main-stream shock can be affected by the jet in two significantly different ways. One way is simply to move the strong shock away from the body without altering its shape. The second and perhaps more interesting case occurs when the jet causes a large displacement of the main shock and considerably changes its shape. It was found that the ratio of jet total pressure to free-stream total pressure necessary to obtain the large displacements of the main-stream shock depended on the ratio of body diameter to jet-exit diameter and also on the jet-exit mach number. The maximum amount the shock could be displaced in percent of body diameter was seen to increase with increasing jet-exit mach number and also with decreasing ratio of body diameter to jet-exit diameter. For the models that were investigated through an angle-of-attack range, the displacement became very unsteady and fell off sharply as the angle of attack was increased. Simplified theoretical considerations applied to the shock-displacement phenomena provide a possible explanation for the two different types of main-stream shock displacement. Theoretical curves show the regions where these types of displacement would occur for different exit mach numbers and pressure ratios for a forward-facing jet in a mach 6 stream."},
{"url":"cran.html#doc917","title":"A method of calculating the short period longitudinal stability derivatives of a wing in linearised unsteady compressible flow.","description":"Mangler, K.W. Rae R. Aero.2468. A method is developed for the calculation of the pressure distribution and the aerodynamic forces and moments on a wing performing harmonic pitching and heaving oscillations. The calculation is based on the assumption of inviscid potential flow without shock waves and is restricted to small incidence, so that the linearized theory is valid. In contrast to other work in the field the theory applies to all mach numbers. It is restricted to small values of the reduced frequency and should be valid for the usual range of short periods occurring at present in flight. The formal solution yields two integral equations for the parts of the load, which are in phase and go out of phase with the oscillation,. These are of the same form as the corresponding equation in steady flow. The way is thus opened for solutions over the whole mach number range at small frequencies, if the corresponding steady solutions can be found. The calculation is in fact easiest for m = 1 and has been done here for delta-wings to supplement a previous supersonic calculation, made on different frequency assumptions, which broke down near m = 1. It appears from the two sets of results that the short period oscillation will be unstable near m = 1, if the apex angle of the delta wing is greater than about 60. This confirms a now generally recognised trend. Such results near m = 1 must of course be invalidated to an unknown extent by thickness viscosity and shock waves at their maximum effect. Nevertheless it is unlikely that these factors will remove the critical nature of the transonic damping as calculated by this method. With all its obvious limitations this method, when extended to other planforms, should provide a useful tool in studying the effect of geometrical parameters on the stability of an aircraft at transonic speeds."},
{"title":"An experimental investigation of the flow over blunt-nosed cones at a mach number of 5. 8.","url":"cran.html#doc423","description":"Machell, R.M. And O'bryant, W.T. Guggenheim aero. Lab. Memo 32, 1956. 8. Shock shapes were observed and static pressures were measured on spherically-blunted cones at a nominal mach number of 5.8 over a range of reynolds numbers per inch from 97, 000 to 238, 000, for angles of yaw from 0 to 8. Six combinations of the bluntness ratios 0.4, 0.8, and 1.064 with the cone half angles 10, 20, and 40 were used in determining the significant parameters governing pressure distribution. The pressure distribution on the spherical nose for both yawed and unyawed bodies is predicted quite accurately by the modified newtonian theory given by, where is the angle between the normal to a surface element and the flow direction ahead of the bow shock. Cone half angle was found to be the significant parameter in determining the pressure distribution near the nose-cone junction and over the conical afterbody. On the 40 spherical nosed cone models the flow overexpanded with respect to the taylor-maccoll pressure in the region of the spherical-conical juncture, after which the pressure returned rapidly to the taylor-maccoll value. For models with smaller cone angles the region of minimum pressure occurred farther back on the conical portion of the model, and the taylor-maccoll pressure was approached more gradually. The shape of the pressure distributions as described in nondimensional coordinates was independent of the radius of the spherical nose and of the reynolds number over the range of reynolds number per inch between.97 x 10 and 2.38 x 10. Integrated results for the pressure foredrag of the models at zero yaw compared very closely with the predictions of the modified newtonian approximation, except for models with large cone angles and small nose radii, where the drag approaches the value given by the taylor-maccoll theory for sharp cones."},
{"url":"cran.html#doc1119","title":"Plastic stability theory of thin shells.","description":"Gerard, G. J. Ae. Scs. 24, 1957. Considerable interest is currently centered on the role of deformation and flow types of plasticity theories in the solution of stability problems. For thin flat plates, deformation theory combined with classical stability theory appears to yield results which are in substantially good agreement with test data. On the other hand, flow or incremental theories appear to require the introduction of initial imperfections in order to obtain a satisfactory degree of correlation with tests. Thus, in view of the current state of development of plastic stability theory, it appears fruitful to exploit the mathematical simplicity inherent in deformation theory in the investigation of the plastic stability of thin shells. Although there may be theoretical objections to deformation theories as a class, test data on flat plates do suggest the predictive value of the results obtained from this theory. In this paper, a set of equilibrium differential equations for the plastic buckling of thin shells of constant unequal radii is derived. This set of three equations applies to flat plates, cylinders, and spheres under any loading system leading to buckling. For particular problems such as buckling of cylinders under axial compression, torsion or lateral pressure, and spheres under external pressure, the set of equations can be reduced to a single eighth-order partial differential equation of the donnell type in terms of the radial displacement only. These donnell-type equations are used to obtain solutions for plastic buckling of spheres under external pressure and long and moderate length cylinders under lateral pressure or torsion loads. The limiting cases of a simply supported flat plate under compression or shear, represent the solutions for short cylinders under lateral pressure or torsion, respectively."},
{"description":"Chapman, D.R., kuehn, D. M. And Larson, H. K. Naca report 1356 Experimental and theoretical research has been conducted on flow separation associated with steps, bases, compression corners, curved surfaces, shock-wave boundary-layer reflections, and configurations producing leading-edge separation. Results were obtained from pressure-distribution measurements, shadow-graph observations, high-speed motion pictures, and oil-film optics. The maximum scope of measurement encompassed mach numbers between 0.4 and 3.6, and length reynolds numbers between 4000 and 5000000. The principal variable controlling pressure distribution in the separated flows was found to be the location of transition relative to the reattachment and separation positions. Classification is made of each separated flow into one of three regimes.. And /turbulent/ with transition upstream of separation. By this means of classificaiton it is possible to state rather literal results regarding the steadiness of flow and the influence of reynolds number within each regime. For certain pure laminar separations a theory for calculating dead-air pressure is advanced which agrees well with subsonic and supersonic experiments. This theory involves no empirical information and provides an explanation of why transition location relative to reattachment is important. A simple analysis of the equations for interaction of boundary-layer and external flow near either laminar or turbulent separation indicates the pressure rise to vary as the square root of the wall shear stress at the beginning of interaction. Various experiments substantiate tnis variation for most test conditions. An incidental observation is that the stability of a separated laminar mixing layer increases markedly with an increase in mach number. The possible significance of this observation is discussed.","title":"Investigation of separated flows in supersonic and subsonic streams with emphasis on the effect of transition.","url":"cran.html#doc187"},
{"title":"The problem of obtaining high lift-drag ratios at supersonic speeds.","url":"cran.html#doc1380","description":"Clinton E. Brown and francis E. Mclean Langley research center, nasa The importance of the lift to drag ratio is well known to all aircraft designers since it gives, to a great extent, the aerodynamic efficiency of the airplane. Aerodynamic efficiency, however, is only one component of the grand compromise that a completed airplane represents. At subsonic speeds, lift-drag ratios of well over 200 have been measured in wind tunnels on airfoil sections., but few powered aircraft have attained (lift to drag ratio) value of 20. It is invariably true that the requirements of stability and control, structure, and flight operation all contribute to reducing the design (lift to drag ratio) considerably below those exotic values which can be predicted from unrestricted aerodynamic theory. If, however, a certain range or operating efficiency is required, there is most certainly a minimum if we examine the range equation we see that range is proportional to the lift-drag ratio, the thermopropulsive efficiency, and the logarithm of the initial to final weight ratio. The appearance of the lift-drag ratio as a linear factor in the range equation indicates that every attempt should be made to increase (lift to drag ratio)., however, the search for higher (lift to drag ratio) may lead to strange and unorthodox configurations. Most frequently, such configurations are ruled out by the adverse effects of their geometry on the weight ratios. In the present paper, we will deal with the maximum lift-drag ratio problem for conventional configurations having a wing and a body in close proximity to each other. No attempt will be made to select a particular configuration as being the best. However, the promising direction to go from the aerodynamic view will be stressed with the understanding that the other factors may outweight the aerodynamics."},
{"description":"Braslow, A.L. Nasa tn.d53, 1959. An investigation was made in the langley 4 by 4-foot supersonic pressure tunnel at mach numbers of 1.61 and 2.01 to determine (1) the effect of distributed roughness on boundary-layer transition with the model surface at adiabatic wall temperature and cooled and (2) the effect of surface cooling on the lateral spread of turbulence. Both distributed granular-type and single spherical roughness particles were used, and transition of the boundary layer was determined by hot-wire anemometers. The transition-triggering mechanism of the three-dimensional roughness at supersonic speeds appeared to be the same as that previously observed at subsonic speeds. In fact, the critical value of the roughness reynolds number parameter (that is, the value at which turbulent spots are initiated by the roughness) was found to be approximately the same at supersonic and subsonic speeds when complete local conditions at the top of the roughness, including density and viscosity, were considered in the formulation of the roughness reynolds number. For three-dimensional roughness at a reynolds number less than its critical value, the roughness introduced no disturbances of sufficient magnitude to influence transition. Surface cooling, although providing a theoretical increase in stability to small disturbances, did not increase to any important extent the value of the critical roughness reynolds number for three-dimensional roughness particles. Cooling, therefore, because of its effect on the boundary-layer thickness, density, and viscosity actually promoted transition due to existing three-dimensional surface roughness for given mach and reynolds numbers. The measured lateral spread of turbulence in the boundary layer appeared to be unaffected by the increased laminar stability derived from the surface cooling.","title":"Effect of distributed three-dimensional roughness and surface cooling on boundary layer transition and lateral spread of turbulence at supersonic speeds.","url":"cran.html#doc80"},
{"url":"cran.html#doc62","title":"Similar solutions for the compressible laminar boundary layer with heat transfer and pressure gradient.","description":"Cohen, C.B. And Reshotko, E. Naca tn.3325, 1955. Stewartson's transformation is applied to the laminar compressible boundary-layer equations and the requirement of similarity is introduced, resulting in a set of ordinary nonlinear differential equations previously quoted by stewartson, but unsolved. The requirements of the system are.. Prandtl number of 1.0, linear viscosity-temperature relation across the boundary layer, an isothermal surface, and the particular distributions of free-stream velocity consistent with similar solutions. This system admits axial pressure gradients of arbitrary magnitude, heat flux normal to the surface, and arbitrary mach numbers. The system of differential equations is transformed to an integral system, with the velocity ratio as the independent variable. For this system, solutions are found for pressure gradients varying from that causing separation to the infinitely favorable gradient and for wall temperatures from absolute zero to twice the free-stream stagnation temperature. Some solutions for separated flows are also presented. For favorable pressure gradients, the solutions are unique. For adverse pressure gradients, where the solutions are not unique, two solutions of the infinite family of possible solutions are identified as essentially viscid at the outer edge of the boundary layer and the remainder essentially inviscid. For the case of favorable pressure gradients with heated walls, the velocity within a portion of the boundary layer is shown to exceed the local external velocity. The variation of a reynolds analogy parameter, which indicates the ratio of skin friction to heat transfer, is from zero to 7.4 for a surface of temperature twice the free-stream stagnation temperature, and from zero to 2.8 for a surface held at absolute zero where the value 2 applies to a flat plate."},
{"title":"The effect of a central jet on the base pressure of a cylindrical afterbody in a supersonic stream.","url":"cran.html#doc173","description":"Reid, J. And Hastings, R.C. Arc r + M.3224, 1962. This report describes an experimental investigation of the factors affecting the base flow and jet structure behind a cylindrical after-body with a central nozzle. Seven interchangeable nozzles were tested. Six of these were convergent-divergent, with a design mach number of 2.0, jet base diameter ratios ranging from 0.2 to 0.8 and nozzle divergence angles ranging from convergent with a jet base diameter ratio of 0.6. In the main experimental programme the free-stream mach number was 2.0 and the boundary layer was turbulent both on the after-body and in the nozzle. Measurements were made of the base pressure, the surface pressure distribution inside the nozzle, the overall thrust and the nozzle mass flow, over a range of jet pressures. This programme was supplemented by comparative tests with the jet exhausting into still air (static tests). Readings were taken of the internal nozzle pressures and the jet thrust at different jet pressures. Schlieren photography was used extensively throughout. The results of the tests with external flow are presented in the form of curves showing the separate effects of jet pressure ratio, jet base diameter ratio, nozzle design mach number and nozzle divergence angle on the base pressure and overall thrust. The special case of base bleed is discussed separately. Similar curves are included for the static tests. These show the effect of jet pressure ratio and nozzle geometry on the jet thrust. A general method of correlating data on annular base pressures is proposed and discussed. Essentially, this method compares the pressure on an annular base with the calculated pressure on the corresponding two-dimensional base. It correlates the present results reasonably well, but is less successful when applied to more extensive data."},
{"description":"Bloxson, D.E. And Rhodes, B.V. J. Ae. Scs.1962. Inverted hemispheres, circular discs (normal to stream), spheres, 26 total angle 0.368 blunt hemisphere cones, 18 total-angle sharp cones, and other axisymmetric shapes were run in a hypervelocity wind tunnel. Hypersonic drag coefficients at zero angle of attack were measured in the air velocity range, 7, 000- efficient is defined as drag force. Knudsen number is defined as mean free path behind shock sphere shock detachment distance. In the case of nonsphere shapes, the knudsen number is defined as the knudsen number of a sphere with the same base diameter. These drag coefficients cover the range of gasdynamics to free molecule flow and are given in graphical form. The drag coefficients were measured by means of a ballistic balance in millisecond intervals, and referenced to the drag coefficient of a sphere in the gasdynamics region, for a gamma of 1.4, of 0.92. Tunnel stagnation conditions of pressure, temperature, density, and pressure drop with time were measured directly. In the tunnel test section, velocity, q density, total pressure, and static pressure were measured directly. These experimental curves have been found useful in the analysis of complex shapes if the complex shapes can be easily broken down into simple components with small interactions between components. Heat-transfer distributions have also been obtained on these and other complex shapes in the hypervelocity wind tunnel, by means of a special paint which changes through several visible spectral orders within a heat transfer range of x10 for a single application. Heat transfer rates, so obtained, have been performed in the hypersonic gasdynamic and slip flow regions and are presented for spheres. These data, in the vorticity interaction region, agree with the data of ferri and zakkay.","url":"cran.html#doc1204","title":"Experimental effect of bluntness and gas rarefaction on drag coefficients and stagnation heat transfer on axisymmetric shapes in hypersonic flow."},
{"title":"Aerodynamic effects of some configuration variables on the aeroelastic characteristics of lifting surfaces at mach numbers from 0. 7 to 6. 86.","url":"cran.html#doc685","description":"Hanson, P.W. Nasa tn.d984, 1961. 7 to 6. 86. Results of flutter tests on some simple all-movable-control-type models are given. One set of models, which had a square planform with double-wedge airfoils with four different values of leading- and trailing-edge radii from 0 to 6 percent chord and airfoil thicknesses of 9, 11, at mach numbers from 0.7 to 6.86. The bending-to-torsion frequency ratio was about 0.33. The other set of models, which had a tapered planform with single-wedge and double-wedge airfoils with thicknesses of 3, 6, 9, and 12 percent chord, was tested at mach numbers from 0.7 to 3.98 and a frequency ratio of about 0.42. The tests indicate that, in general, increasing thickness has a destabilizing effect at the higher mach numbers but is stabilizing at subsonic and transonic mach numbers. Double-wedge airfoils are more prone to flutter than single-wedge airfoils at comparable stiffness levels. Increasing airfoil bluntness has a stabilizing effect on the flutter boundary at supersonic speeds but has a negligible effect at subsonic speeds. However, increasing bluntness may also lead to divergence at supersonic speeds. Results of calculations using second-order piston-theory aerodynamics in conjunction with a coupled-mode analysis and an uncoupled-mode analysis are compared with the experimental results for the sharp-edge airfoils at supersonic speeds. The uncoupled-mode analysis more accurately predicted the flutter characteristics of the tapered-planform models, whereas the coupled-mode analysis was somewhat better for the square-planform models. For both the uncoupled- and coupled-mode analyses, agreement with the experimental results improved with increasing mach number. In general, both methods of analysis gave unconservative results with respect to the experimental flutter boundaries."},
{"url":"cran.html#doc1225","title":"The effect of adverse pressure gradients on the characteristics of turbulent boundary layers in supersonic streams.","description":"George H. Mclafferty and robert E. Barber United aircraft corporation research laboratories Tests were conducted at mach numbers from 2.0 to 3.5 to determine the thickness and profile shape characteristics of turbulent boundary layers on two-dimensional and axisymmetric curved-surface models having adverse pressure gradients. The magnitude of the gradients relative to the boundary-layer thickness at the beginning of the gradient was varied by employing models having different radii of curvature and by changing the boundary-layer thickness at the beginning of the gradient. The overall pressure rise in most cases was greater than the value which would cause a turbulent boundary layer to separate if the pressure rise were created by an oblique shock wave. An analytical investigation was also conducted so that the results of the experimental investigation could be applied to the prediction of cases outside the range of the experiments. It is shown that boundary-layer momentum thickness can be predicted from the von karman boundary-layer momentum equation, but that measured values of boundary-layer profile shape are in poor agreement with values computed from procedures derived by extending conventional methods for predicting profile shape in subsonic flow. A new procedure for calculating boundary-layer profile shapes, developed in this paper, is shown to provide a good correlation between experimental and calculated values of boundary-layer profile shapes in adverse pressure gradients created by curved surfaces. This procedure is based on the experimental observation that the station at which high-energy free-stream flow actually mixes into a turbulent boundary layer in an adverse pressure gradient is well downstream of the station at which flow would have to mix in order to maintain a flat-plate profile."},
{"title":"Aerodynamic heating of blunt nose shapes at mach numbers up to 14.","url":"cran.html#doc1104","description":"Stoney, W.E. Naca rm l58 e05a, 1958. Results are presented from recent investigations of the aerodynamic heating rates of blunt nose shapes at mach numbers up to 14. Data obtained in flight and wind-tunnel tests have shown that the flat-faced cylinder has about 50 percent the stagnation-point heating rates of the hemisphere over nearly the entire mach number range. Tests made at a mach number of 2 on a series of bodies made up of hemispherical segments of varying radius of curvature showed that slight amounts of curvature can decrease the local rates at the edge of the flat-faced cylinders with only a slight increase in the stagnation rate. The total heat transfer to such slightly curved bodies is also somewhat smaller than the total heat transfer to flat-faced cylinders. Comparison of several tests with theoretical heating-rate distributions showed that both laminar and turbulent local rates can be predicted by available theories /given the pressure distribution about the body/ reasonably well, although the scatter of the available data still leaves open the choice between the theories at the edge of the bodies, where they usually differ. Tests on a flat-faced cylinder at a mach number of 2.49 and at angles of attack up to 15degree showed the movement of the apparent stagnation point from the center of the body to the 50 percent windward station at creased about 30 percent while that near the leeward edge decreased about 20 percent at 15degree angle of attack. Preliminary results on a concave nose have indicated the possibility that this type of design may be developed to give heating rates significantly lower than even the flat-faced cylinder rates. The test results have also shown, however, the existence of an unsteady flow phenomenon which can increase the heating rates to extremely high values."},
{"description":"Love, E.S. Naca rm l52119a, 1952. An investigation has been made at a mach number of 1.62 to determine the effects of a small jet of air exhausting from the nose of an elliptical body of revolution upon boundary-layer transition and the viscous, pressure, and total drag of the forebody at three body stations body nose were also obtained. The tests were conducted at reynolds numbers of 2.13 x 10 and 7.66 x 10, based on body length. The maximum range of thrust coefficients for the small jet was from 0 to about at the lower test reynolds number, for which the boundary layer was laminar over the entire body in the jet-off condition, a very small flow from the jet moved the point of transition forward to the vicinity of the 20-percent-body station. As the jet flow was increased, the transition point moved abruptly to the nose at a thrust coefficient of about gardless of the type of boundary layer. At the higher test reynolds number for which the boundary layer was largely turbulent in the jet-off condition the total drag, including skin friction, was reduced somewhat by the action of the jet. Although the forward-exhausting small jet was found to have the above favorable effects upon the drag, these findings are not believed too important since the question arises as to the benefits of the same small jet exhausting from the rear of the body in the conventional manner. No attempt was made to establish geometric optimums in the present investigation, yet, from a general consideration of the benefits indicated by the present results and the phenomena known to occur in the vicinity of rearward-exhausting jets, the benefits of a small jet exhausting rearward would appear to exceed those of the same small jet exhausting forward, particularly so when the flow over the body is laminar in the jet-off condition.","url":"cran.html#doc992","title":"The effects of a small jet of air exhausting from the nose of a body of revolution in supersonic flow."},
{"description":"Resler, E.J. And Sears, W.R. J. Ae. Scs. 25, 1958, 235. The equations describing the flow of an electrically conducting fluid in the presence of electric and magnetic fields are written down with the aid of certain simplifications appropriate to aeronautical applications. In order to estimate the probable significance of magneto-aerodynamic effects, some data on conductivity of pure and /seeded/ air are first examined. Dimensionless quantities representing the ratios of forces and of currents are then formed and their values studied for conditions of flight in the atmosphere. Some examples of magneto-hydrodynamic and magneto- gasdynamic effects in simple flows are given. These include two cases of poiscuille flow of conducting liquids with applied magnetic fields and the case of quasi-one-dimensional gas flow with applied electrical and magnetic fields. In the last case, attractive possibilities are found for controlled acceleration or deceleration of gas at subsonic and supersonic speeds, even in constant-area channels. The behavior of the flow is characteristically different in different regimes of mach number and flow speed relative to certain /significant speeds/ that are dependent on the ratio of electrical to magnetic field strengths. These are studied, and a chart is constructed to relate the length to the speed ratio of a maximum-acceleration constant-area channel. It is concluded that the advantages that may accrue from magneto-aerodynamic methods are sufficiently attractive to justify the considerable research and engineering development that will be required. Among the unsolved engineering problems are the reduction of surface resistance of electrodes in contact with a conducting gas, development of techniques for seeding, and provision of the required magnetic fields in flight.","url":"cran.html#doc33","title":"The prospects for magneto-aerodynamics."},
{"description":"Crabtree, L.F. Rae tn. Aero.2695, 1960. A survey is made of existing theories for the calculation of pressure distributions on slender bodies at hypersonic speeds. No account is taken of boundary layer displacement effects which are expected to become important above a mach number of about 10 for a slender body. First the breakdown of linearised supersonic theory is demonstrated as mach number increases above about 5, and this is followed by a derivation of the hypersonic similarity rule. This section includes a description of the piston-analogy. Next a physical interpretation of hypersonic flow is outlined and a simple derivation of the modified newtonian pressure formula is given. The equations of flow through an oblique shock wave are simplified by assuming a strong shock, and various results are thereby derived. These include the tangent-wedge and tangent-cone formulae. This is followed by a description of the newtonian approximation for slender bodies, including the effect of centrifugal forces, and the connection with newtonian flow theory is emphasized for. The shock-expansion method is described in some detail for both two-and three-dimensional bodies, and finally some remarks are made about the available data sheets and tables for estimating pressures on cones and ogive-cylinders in yaw. The note does not claim to be original, even in presentation. The aim has been to prepare a reasonably complete survey of available theory for hypersonic flow over slender bodies, excluding viscous and explicit real gas effects. This will provide the background for further work in which experimental data will be analysed and in conjunction with which it is hoped to produce accurate design methods for estimating pressures and forces on shapes intended for sustained flight at hypersonic speeds.","url":"cran.html#doc1310","title":"Survey of inviscid hypersonic flow theory for geometrically slender shapes."},
{"title":"An investigation of lifting effects on the intensity of sonic booms.","url":"cran.html#doc811","description":"Morris, J. J. Roy. Aero. Soc. 64, 1960, 610. This paper is a brief summary of an investigation made to check the effect of lift on the shock noise of aircraft flying at supersonic speeds. The method of hayes has been combined with the theory of whitham to predict the asymptotic shock strength of wings carrying lift and of combinations of bodies and lifting wings. (a similar, but not quite as general, method was derived by walkden in ref. 6.) whitham's formula, including only the volume term, has been used extensively to predict the boom intensity of aeroplane type bodies and the agreement with experiment has, so far, been quite reasonable. The test data obtained to date extends only up to about 40, 000 ft. Altitude and the calculations of this paper show that under those conditions the shock noise of the aircraft tested so far will, in most cases, be dominated by the volume term. It is shown that at higher altitudes lifting effects will dominate for even the small fighter and they will dominate over most of the altitude range for large bomber and supersonic transport aircraft. The boom intensity due to lift decreases with altitude as which compares to in the volume case (=pressure at altitude h). It is insensitive to mach number, wing loading, wing plan shape and lift distribution. A simple rule for calculating the shock noise due to combined volume and lifting effects is proposed which is applicable to configurations with wings located towards the rear of the fuselage. The rule states that the shock noise of an aircraft carrying lift is equal to the shock noise due to volume (neglecting lift) or the shock noise due to lift (neglecting volume), whichever is the greater. A chart is presented from which rapid estimates can be made of the shock noise of lifting wing-body combinations."},
{"description":"Duncan, W.J. R + m 1425, july 1931. The use of model tests in the prediction of full-scale critical flutter speeds is now well established, and the technique of such tests is therefore worthy of discussion. In order to obtain critical speeds for the model within the speed range of ordinary wind tunnels it is necessary that the model should differ in some respect from a mere small suggested by mckinnon wood the modification of the model consists in a reduction of its effective stiffnesses. This method has the defect /in most cases probably not serious/ that the model experiment is conducted at a reynolds number much below that for full-scale. In the present paper it is pointed out that an alternative method of reducing the critical speed is to increase the mass loading of the model and to make the flutter tests in compressed air. * it is then quite feasible to reach the full-scale reynolds number. This method of reducing the critical speeds by a proportionate increase of all effective densities may also be combined with a reduction of the elasticity of the model. The relation of model and full-scale stresses at the critical flutter speeds is considered. Where the reduction in critical speed is effected by increase of density only, the model and full-scale stresses are equal. In a model of reduced elasticity the stresses in the wires are the same as for full-scale, whereas, the stresses in the spars are less than for full-scale. This is in accord with the usual experience that the wires of such a model are the first parts of the structure to fail in a flutter. Lastly, the influence of gravity on flutter is considered. This is negligibly small for full-scale, but not necessarily so for the model. Gravitational effects can sometimes be corrected by suitable orientation of the model.","url":"cran.html#doc874","title":"The use of models for the determination of critical flutter speeds."},
{"description":"King-hele, D.G., and cook, G.E. Rae tn.space 18, 1962. Pt.iv with scale height dependent on altitude. The effect of air drag on satellite orbits of small eccentricity e was studied in part i (tech. Note gw 533), on the assumption that atmospheric density varies exponentially with distance r from the earth's centre, so that the 'density scale height' h, defined as, is constant. In practice h varies with height in an approximately linear manner, and in the present note the theory is developed for an atmosphere in which h varies linearly with R. Equations are derived which show how perigee distance and orbital period vary with eccentricity, and how eccentricity varies with time. Expressions are also obtained for the life-time and air density at perigee in terms of the rate of change of orbital period. The results are also presented graphically. The results are formulated in two ways. The first is to specify the extra terms to be added to the constant-h equations of part I. The second the best constant value of h for use with the equations of part I. For example, it is found that the constant-h equations connecting perigee distance (or orbital period) and eccentricity can be used unchanged without loss in accuracy, if h is taken as the value of the variable h at a height above the mean perigee height during the time interval being considered, where, and decreases from to 0 as e decreases from 0.02 to 0. Similarly the constant-h equations for air density at perigee can still be used if h is evaluated at a height above perigee, where, and decreases to zero as e decreases from constant-h equations can still be used if h is evaluated at the scale height below the initial height. Variation of h with altitude has a small effect on the lifetime - about 3 - and on the e-versus-time curve.","title":"The contraction of satellite orbits under the influence of air drag. Pt.iv with scale height dependent on altitude.","url":"cran.html#doc548"},
{"title":"Static aerodynamic characteristics of a short blunt 10 semi-vertex angle cone at a mach number of 15 in helium.","url":"cran.html#doc947","description":"Fohrman, M.J. Nasa tn.d1648, 1963. Axial force, normal force, pitching moment, and shock-wave shape were determined for a body of revolution consisting of a short blunt 10 semivertex angle cone with a flat base and also with a conical afterbody having a semi-vertex angle of 50. Measurements were made in helium at a free-stream mach number of 15 and a free-stream reynolds number of 2.25x10 based on maximum body diameter over an angle-of-attack range from the configuration with the conical afterbody was statically stable in the nose-forward attitude only, whereas the configuration with no afterbody was statically stable in both the nose-forward and base-forward attitudes. The force and moment data of both shapes were predicted reasonably well by modified newtonian theory at all angles of attack, except the pitching-moment coefficient for the model without afterbody near 180 angle of attack. In this region, measurements indicated static stability, whereas theory indicated static instability. The helium data agreed reasonably well with a limited amount of force and moment data obtained in a ballistic range at small angles of attack in air at a mach number of 15 and also with force and moment data obtained in air over a complete angle-of-attack range at a mach number of 5.5. The value of axial-force coefficient and the shape of the bow shock wave at zero angle of attack for both models obtained from a numerical flow field calculation agreed very well with the data. The value of the axial force coefficient at 180 angle of attack for the model with afterbody agreed reasonably well with the theoretical value for a cone. The position and shape of the shock envelope near the stagnation point also could be predicted accurately by an approximate method over an angle-of-attack range from"},
{"title":"On transverse vibrations of thin, shallow elastic shells.","url":"cran.html#doc1039","description":"An experimental investigation was made (1) to evaluate previously published theoretical procedures for the prediction of stress distribution for cases of radially symmetric abrupt change in wall thickness of thin-walled cylinders subject to internal pressure and (2) to investigate the significance of stresses attributable to the presence of thickness changes typical of design practice. One theory was adequate in itself for solution of the case of continuous middle surface,. Use of the second theoretical procedure was required to determine the additional stresses arising from discontinuous middle surfaces at the change in thickness. Comparisons were made between theoretical and experimental stress distributions for cases with continuous middle and continuous inner surfaces for radially symmetric changes in wall thickness of a cylinder subject to internal pressure for diameter to larger wall thickness ratios of 117 and 28 and for the case of a continuous outer surface for a ratio of 28. In all tests the ratio of wall thicknesses at the change in wall thickness was 0.4. There was reasonably good correlation between theoretical and experimental curves of stress distribution. On the basis of this correlation, it was concluded that the applicable theories were valid. It was shown that inclusion of the stresses arising from the condition of discontinuous middle surfaces at a change in thickness has an important effect on stress distribution. In the case of a cylinder with a continuous outer surface, the maximum mean effective stress was of sufficient magnitude to indicate that this geometry should be avoided in design if possible. The maximum mean effective stress was not increased to a significant degree by the presence of a change in wall thickness in the other cases."},
{"title":"Extension of boundary layer separation criteria to a m=6.5 utilizing flat plates with forward-facing steps.","url":"cran.html#doc996","description":"Sterrett, J.R. And Emery, J.C. Nasa tn.d618, 1960. 5 utilizing flat plates with forward-facing steps. An experimental investigation has been made of the separation phenomena on a flat plate to which forward-facing steps were attached to force separation. Both laminar and turbulent flows were investigated over a mach number range of approximately distributions, shadowgraph and chemical film techniques, the pressure rise at separation, the laminar plateau pressure, and the turbulent peak pressure were determined. Boundary-layer surveys were made on a smooth flat plate and on a flat plate with roughness to force transition. Examinations of the separated flow showed that the predominant variable in the determination of the pressure distribution was the location of transition relative to the separation point and reattachment. Pure laminar, transitional, and turbulent types of separation were found in this mach number range. The peak static-pressure-rise ratios for identical forward-facing steps at a mach number of 6.25 were approximately 1.5 and 5.0, respectively, for pure laminar and turbulent separation. The effect of reynolds number on the peak pressure rise for turbulent separation for the lower mach number range was found to be very minor provided the step height was of the order of the boundary-layer thickness. As the mach number is increased, the peak pressure coefficient for turbulent separation decreased from approximately 0.18 at a mach number of 4 to about 0.13 at a mach number of 6.25. The pressure coefficient at the separation point for laminar separation decreases from approximately 0.014 at a mach number of value at a mach number of 6.5. The results obtained with forward-facing steps agree with the trends predicted, based upon lower mach number studies."},
{"title":"Stresses from local loadings in cylindrical pressure vessels.","url":"cran.html#doc1175","description":"Bijlaard, P.P. Asme trans. 77, 1953. A short discussion is given of the possible methods for computing the stresses caused in cylindrical shells by local loadings. It is concluded that the method of developing the loads and displacements into double fourier series leads to formulas which are best suited for numerical evaluation. With this method the pertinent expressions for the displacements caused by radial loads are found by reducing the three partial differential equations of the shell theory to an eighth-order differential equation in the radial displacements, which is similar to, but not identical with, those derived by donnell and yuan. Insertion of the fourier series for the radial displacements and the external loading in this equation leads directly to a double series expression of the radial displacement w in terms of the load factors of the radial load. This results in the pertinent expressions for the other displacements and for the bending moments and membrane forces. The cases of radial loading considered here and those which can be reduced to it are (a) a load uniformly distributed within a rectangle, tion, uniformly distributed over a short distance in the circumferential direction, (d) a moment in the circumferential direction, uniformly distributed over a short distance in the longitudinal direction. For all these loadings the load factors, which have to be used in the pertinent formulas for the displacements, bending moments, and membrane forces, are computed. For the case of tangential loading an eighth-order differential equation is derived in terms of the radial displacement and the tangential load. Using this equation, formulas for the displacements, bending moments, and membrane forces for tangential loading within a rectangle are found."},
{"description":"Yen, K.T. And Toba, K. J. Ae. Scs. 1961, 877. The purpose of this paper is to present a theory to account for surface curvature effects on the two-dimensional boundary-layer flow which approaches a potential flow at free stream. The problem of two-dimensional viscous flow is first formulated by using the streamlines and their orthogonal trajectories as the generalized coordinates. A boundary-layer approximation is applied to the navier-stokes equations and the gauss equation in the generalized coordinates to yield the boundary-layer equations. The conditions under which similar solutions of the boundary-layer equations exist are determined. By a simple transformation, the governing differential equation can be expressed in a form which reduces to the falkner-skan equation for zero surface curvature. Numerical results for a similar solution which corresponds to a flow over a curved surface with zero surface pressure gradient have been obtained. The velocity profiles in the boundary layer and the wall skin-friction distribution for concave and convex surfaces are presented. The wall skin friction for a convex wall is found to be higher than the blasius value for a flat plate. On the other hand, for a concave wall, the skin friction will drop below the blasius value as the curvature increases, but it appears to reach a minimum, and beyond this minimum point it will increase again. The same flow problem was treated by murphy by a different method of analysis. Comparison of murphy's results with those obtained by the present method reveals some basic differences in the boundary-layer characteristics. In particular, murphy's results indicate that the wall skin friction for a convex surface is smaller than the blasius value, while for a concave wall it is higher.","title":"A theory of the two dimensional laminar bounary layer over a curved surface.","url":"cran.html#doc1235"},
{"description":"Seiff, A. Nasa tn.d1304, 1962. When a ramp or other compression surface is located in a locally supersonic region behind a hypersonic bow shock wave, it generates a secondary shock wave. The ramp flow disturbance may be viewed as an embedded newtonian impact flow if the embedded shock layer is thin. Examination of the applicability of newtonian flow theory to cones and wedges in uniform streams suggests that this theory can be expected to give a useful approximation to the surface pressures. A pressure equation based on this concept predicts a number of interesting things.. First, pressures can differ from simple newtonian theory by factors of 1 5 to 3,. For example, on flare stabilizers on blunt-nosed bodies of revolution, pressures are lower than newtonian and diminish with increasing flight speed in the hypersonic speed range. The calculated pressures vary over the flare surface as a result of the nonuniformity of its incident stream, and depend on the axial location of the flare. In the case of a flap mounted on a large-angled blunt-nosed cone, the pressure coefficients vary from 1 to 5 through the variable entropy layer. A pressure coefficient of 5 greater than the maximum possible in newtonian flow can occur because the compression process is more efficient than a single shock wave process. On areas of the flap that protrude through the main bow wave, the pressure coefficient should revert to the simple newtonian value. Equations are developed for the initial slopes of the normal-force and pitching-moment curves of a flare stabilizer. In the simplest case these differ from conventional newtonian theory by the ratio of local dynamic pressure to free-stream dynamic pressure. This ratio takes values as low as 0.1 in some of the examples considered.","url":"cran.html#doc1356","title":"Secondary flow fields embedded in hypersonic shock layers."},
{"description":"Tan, H.S. J.ae.scs. 1959, 360. The superaerodynamic nose drag of a body in a free-molecule flow involves two parameters.. The speed ratio s between ordered and random molecular motions (modified mach number), and the temperature ratio between the solid surface and undisturbed gas. Simplifications of the drag formula are obtained at hypersonic as well as low-subsonic extremes. To minimize the drag on a nose of specified length and base radius, the ordinary method of calculus of variation was found inadequate. A generalized approach has, accordingly, been developed, and the specification of end conditions is discussed at length. Results of the present investigation indicate that in all cases an optimum nose requires a flat tip. The optimum nose curve for the hypersonic extreme does not depend on the temperature ratio, but that for the low-subsonic extreme varies in the following manner.. For a hot body the curve is convex,. For a cold body, concave. An optimum solution exists in a restricted range of specification only. With prescribed tip and base radii the admissible nose length is bounded below for the cases of hypersonic and low-subsonic hot body and bounded above for the case of low-subsonic cold body. A vanishing tip radius leads to an infinitely long nose in the former and a vanishing nose in the latter case. Optimum nose curves for several temperature ratios at the low-subsonic extreme, as well as the one for hypersonic extreme, are presented. It is observed that at the low-subsonic extreme, with, the hot-body solution asymptotically approaches the hypersonic solution--I.E., a slender conventional warhead with a flat tip,. Whereas with, the cold-body solution asymptotically approaches the minimal-surface solution--I.E., tip radius, a flat disc.","url":"cran.html#doc1373","title":"Nose drag in free-molecule flow and its minimization."},
{"description":"Rose, P.H., probstein, R.F. And Adams, M.C. J. Ae. Scs. 1958, 751. The problem of heat transfer from high-temperature air through a turbulent boundary layer to a cold surface is considered both analytically and experimentally. Heat-transfer data obtained in shock tubes are presented and correlated by a semiempirical theory which includes the effect of atomic diffusion. The distinguishing characteristics of turbulent boundary layers with dissociation and large cooling are considered. It is shown that the equations governing such flow, after certain approximations, can be represented in a form similar to the classical equations for a turbulent boundary layer. An approximate theory is proposed for turbulent heat transfer for a highly cooled boundary layer on portions of the body where the pressure gradient is negligible in the case of blunted bodies of revolution in high-speed flight. Experimental results obtained on the cylindrical portion of a hemisphere-cylinder model are presented for conditions simulating flight speeds to 21, 350 ft. Sec., where up to 30 per cent of the molecules are dissociated. Reynolds numbers of 2.5 x 10, based on local fluid properties external to the boundary layer, were achieved. The larger values of reynolds number and flight speed were not obtained simultaneously, due to structural limitations of the shock tubes,. However, the experiments were conducted in such a way that the important effects of each could be determined. In the experiments the mach number external to the boundary layer varied between 1.7 and 2.2. The corresponding mach number for blunted nonslender bodies in flight would have a maximum value between 2.5 and 4,. However, it is shown that these differences in mach number are not important for such bodies.","url":"cran.html#doc1263","title":"Turbulent heat transfer through a highly cooled, partially dissociated boundary layer."},
{"title":"Turbulent mixing of a rocket exhaust jet with a supersonic stream including chemical reactions.","url":"cran.html#doc1061","description":"Vasilu, J. J. Aero. Sc. V. 29, january 1962, pp 19-28. The equations for the turbulent mixing of a two-dimensional supersonic jet issuing into an ambient supersonic stream are formulated. Both streams consist of a mixture of chemically active and possibly reacting gases, therefore any heat release by chemical reaction is included,. The net mass rate of production of species is obtained on the assumption that the reaction rate constant is given by an expression reducible to the classical arrhenius law. The equations first given in terms of the x, and y coordinates, are expressed in dimensionless form and in terms of the x and coordinates, where is the stream function. The resulting expressions are all of the /heat conduction/ type,. They are put in a finite difference form by using the crank-nicolson method of substituting finite difference approximations for both the /time/ and /space/ derivatives. The mixture is assumed to consist of six species, namely h2o, h2, o2, co2, co, and n2, and the oxidation of h2 and co is assumed to take place according to a single-step chemical reaction. The solution of the problem is based on the simultaneous solution of 8n linear algebraic equations in 8n unknowns, n being the number of internal grid points at every step in the x-direction, and 8 the total number of unknowns at each grid point, namely velocity, temperature, and concentration for each of the six species. A method of obtaining initial and boundary conditions from available inviscid jet flow solutions is discussed. The equations are programed for calculation on an ibm-704 computer. Finally, one typical case is considered, and plots of velocity, temperature, and concentration profiles are given for the initial stages of development of the mixing layer."},
{"title":"Investigation of a systematic group of naca 1 - series cowlings with and without spinners.","url":"cran.html#doc198","description":"Nichols, M.R. And Keith, A.L. Naca r950, 1949. An investigation has been conducted in the langley propeller-research tunnel to study cowling-spinner combinations based on the naca 1-series nose inlets and to obtain systematic design data for one family of approximately ellipsoidal spinners. In the main part of the investigation, 11 of the related spinners were tested in various combinations with 9 naca open-nose cowlings, which were also tested without spinners. The effects of location and shape of the spinner, shape of the inner surface of the cowling lip, and operation of a propeller having approximately oval shanks were investigated briefly. In addition, a study was conducted to determine the correct procedure for extrapolating design conditions determined from the low-speed test data to the design conditions at the actual flight mach number. The design conditions for the naca 1-series cowlings and cowling-spinner combinations are presented in the form of charts from which, for wide ranges of spinner proportions and rates of internal flow, cowlings with near-maximum pressure recovery can be selected for critical mach numbers ranging from spinners and the effects of the spinners and the propeller on the cowling design conditions are presented separately to provide initial quantitative data for use in a general design procedure through which naca 1-series cowlings can be selected for use with spinners of other shapes. By use of this general design procedure, correlation curves established from the test data, and derived compressible-flow equations relating the inlet-velocity ratio to the surface pressures on the cowling and spinner, naca 1-series cowlings and cowling-spinner combinations can be designed for critical mach numbers as high as 0.90."},
{"description":"Gouse, S.W., brown, G.A. And Kaye, J. J. Ae. Scs. 29, 1962, 1250. The purpose of this research program was to investigate the effects of a diffusion field on a laminar boundary layer in a supersonic flow. Specifically, helium, nitrogen, and argon were uniformly injected into the laminar boundary layer of a high-speed flow in a tube with the objective of determining the effects of such injection on the pressure, temperature, and recovery factor distribution along and downstream of the injection region. A continuously operating axially-symmetric wind tunnel has been designed, constructed, and operated. This tunnel consists of an air supply system, a flowmeter, an upstream stagnation tank, a supersonic nozzle (throat diameter 0.262 and exit diameter 1.400), a test section of variable length (zero to 81 diameters, test section diameter of 1.400), a downstream stagnation tank, an exhaust system, a foreign gas supply system, and all necessary instrumentation. The overall performance of this apparatus in terms of the design specifications was excellent. The tunnel was instrumented with 109 thermocouples. All temperatures except ambient temperatures were automatically measured and recorded by means of a self-balancing recording potentiometer. There was 29 pressure taps distributed along the tunnel, 23 along the test section itself. Pressures were measured by means of an interconnected micromanometer and a vacuum referenced manometer system with overlapping ranges. For all of the results reported herein, the overall test section was 41 diameters in length,. Composed of a porous test section approximately 7.2 diameters in length (leading edge approximately 1.8 diameters from the nozzle exit plane) and four nylon test sections of 8 diameters each.","title":"Some effects of injection of foreign gases in a decelerating laminar boundary layer in supersonic flow.","url":"cran.html#doc529"},
{"url":"cran.html#doc1392","title":"The solution of small displacement, stability or vibration problems concerning a flat rectangular panel when the edges are either clamped or simply supported.","description":"Hopkins, H.G. Arc r + M.2234, 1945. This report describes an energy method for the exact solution of problems concerning the small displacements, stability or vibration of a flat rectangular panel when the edges are either clamped or simply supported. The influence of stiffeners which are parallel to one pair of edges, and situated in pairs on opposite sides of the panel so that the neutral axis of each stiffener pair lies in the middle surface of the panel, is taken into account. The method is not only applicable to isotropic panels but also to aeolotropic panels when the material of the panel has two directions of elastic symmetry parallel to the edges. The final solution of the problems depends on an infinite set of linear equations for small displacement problems or on an infinite determinantal equation for stability and vibration problems. The important feature of the analysis given is that it enables a direct approach to be made to these equations in any particular problem. It is not in general possible to obtain a direct solution of the final equations and it is necessary to approximate and consider a finite set of linear equations or a finite determinantal equation derived from the more important terms in the analytical expression for the transverse displacement of the panel. Here, physical intuition and, if available, experimental data serve as a guide and the accuracy of the final results so obtained is gauged by the rate of convergence with the increase in the number of terms considered. The general method of solution is applied first to the free vibration of a square panel when all the edges are clamped, and second to the buckling of a square panel under shear when three edges are clamped and one edge is simply supported."},
{"title":"Design and test of mixed-flow impellers, viii - comparison of experimental results for three impellers with shroud redesigned by rapid approximate method.","url":"cran.html#doc986","description":"Osborn, W.M. Et al. Naca rm e56l07, 1957. Three centrifugal impellers with parabolic, circular, and skewed-parabolic blading were modified by a recently developed design procedure to reduce the velocity gradients along the hub from inlet to outlet. All original dimensions except the shroud contours were retained. Experimental investigation showed that the modified impellers had better performance characteristics than the original impellers at all speeds investigated, the greatest gains occurring at speeds of 1300 feet per second and higher. These large gains probably resulted primarily from more favorable velocity gradients and from designing these impellers further away from the condition necessary for eddy formation. The modified impellers were thus able to operate over a wider range of weight flows at high speeds. The modified impellers were investigated over a range of equivalent speeds of 900 to 1500 feet per second and flow rates from maximum to the point of incipient surge. At 1300 feet per second, the peak pressure ratio and maximum adiabatic temperature-rise efficiency for the parabolic-bladed impeller were 3.07 and 0.825, respectively. For the same conditions, the circular-bladed impeller and the skewed-parabolic-bladed impeller had pressure ratios of 3.13 and 3.15 and efficiencies of 0.737 and 0.805, respectively. Of the three, the parabolic-bladed impeller had the highest maximum efficiencies /0.854 to 0.800/ and the best weight-flow range over the speed range tested. On the basis of the parameters investigated, it appears that parabolic blading is superior to circular blading. The experimental results indicate that the design method of naca tn 3399 is a reliable method for use in designing centrifugal impellers."},
{"url":"cran.html#doc216","title":"The supersonic axial flow compressor.","description":"Kantrowitz, A. Naca r974, 1950. An investigation has been made to explore the possibilities of axial-flow compressors operating with supersonic velocities into the blade rows. Preliminary calculations showed that very high pressure ratios across a stage, together with somewhat increased mass flows, were apparently possible with compressors which decelerated air through the speed of sound in their blading. The first phase of this investigation, which has been reported in naca acr l5d20, was the development of efficient supersonic diffusers to decelerate air through the speed of sound. The present report is largely a general discussion of some of the essential aerodynamics of single-stage supersonic axial-flow compressors. In the supersonic flow about isolated bodies, large energy losses usually occur due to wave systems which extend far from the bodies. Supersonic flow entering a cascade is considered and, in this case, the possibility of entirely eliminating this extended wave system is demonstrated,. Thus, no reason for supersonic compressors to be necessarily inefficient is apparent. The conditions that occur as the flow through the compressor is being started are discussed and a hypothesis as to the type of transonic flow which will be encountered is proposed. As an approach to the study of supersonic compressors, three possible velocity diagrams are discussed briefly. Because of the encouraging results of this study, an experimental single-stage supersonic compressor has been constructed and tested in freon-12. In this compressor, air decelerates through the speed of sound in the rotor blading and enters the stators at subsonic speeds. A pressure ratio of about 1.8 at an efficiency of about 80 percent has been obtained."},
{"description":"Proudman, J. Proc.roy.S.a 214, 1952, 119. A finite region, with fixed boundaries, of an infinite expanse of compressible fluid is in turbulent motion. This motion generates noise and radiates it into the surrounding fluid. The acoustic properties of the system are studied in the special case in which the turbulent region consists of decaying isotropic turbulence. It is assumed that the reynolds number of the turbulence is large, and that the mach number is small. The noise appears to be generated mainly by those eddies of the turbulence whose contribution to the rate of dissipation of kinetic energy by viscosity is negligible. It is shown that the intensity of sound at large distances from the turbulence is the same as that due to a volume distribution of simple acoustic sources occupying the turbulent region. In this analogy, the whole fluid is to be regarded as a stationary and uniform acoustic medium. The local value of the acoustic power output p per mass of turbulent fluid is given approximately by the formula where a is a numerical constant, u is the mean-square velocity fluctuation, is the time, and c is the velocity of sound in the fluid. The constant a is expressed in terms of the well-known velocity correlation function f(r) by assuming the joint probability distribution of the turbulent velocities and their first two time-derivatives at two points in space to be gaussian. The numerical value is then obtained by substituting the form of f(r) corresponding to heisenberg's theoretical spectrum of isotropic turbulence. It is found that the effects of decay make only a small contribution to the value of a, and that the order of magnitude of a is not changed when widely differing forms of the function f(r) are used.","url":"cran.html#doc151","title":"The generation of noise by isotropic turbulence."},
{"description":"Feldman, S. J. Ae. Scs. 28, 1961, 433. The trail left in the atmosphere by a body moving at hypersonic speeds is the subject of theoretical treatment. The times required for ionization and dissociation (and their inverse processes) to go to completion, when compared to the flow times of a gas particle, are important in determining the observable effects of hypersonic trails-I.E., emitted thermal radiation and reflection of electromagnetic waves from the trail. In order to simplify the theoretical treatment, the trail is divided into two regions.. (1) the expansion-controlled trail, which treats the behavior of the wake behind the body up to a point, along the direction of flight, where the pressure decays to the free-stream value and cooling is controlled principally by the expansion of the flow, and (2) the conduction-controlled trail, where the trail cools mainly by diffusion of heat away from the high-temperature core. The influence of the details of the body shape on the observables are discussed and a simple computational procedure for the behavior of the conduction-controlled trail is developed based on integral methods. Results of calculations that assume thermodynamic equilibrium of the flow field give the values of the thermodynamic variables in the trail of a sphere, axial distributions of emitted thermal radiation, and maps of electron density distribution. It is shown that the cooling of the conduction-controlled trail is essentially due to conduction of heat and that viscous effects are not important. It is found that this portion of the trail does not widen as one proceeds downstream. Flight velocities considered vary between 15, 000 and 35, 000 ft sec and altitudes range between 100, 000 and 250, 000 ft.","url":"cran.html#doc85","title":"On trails of axisymmetric hypersonic blunt bodies flying through the atmosphere."},
{"url":"cran.html#doc1092","title":"Wing-nacelle-propeller interference for wings of various spans. Force and pressure distribution tests.","description":"Robinson, R.G. And Herrnstein, W.H. Naca R.569, 1936. Force and pressure distribution tests. An experimental investigation was made in the N. A. C. A. Full-scale wind tunnel to determine the effect of wing span on nacelle-propeller characteristics and, reciprocally, the lateral extent of nacelle and propeller influence on a monoplane wing. The results provide a check on the validity of the previous research on nacelles and propellers with 15-foot-span wings tested in the the scale propeller and the N. A. C. A. Cowling used in the former researches were tested in three typical tractor locations with respect to a thick wing of 5-foot chord and 30-foot span. The span was progressively reduced to 25, 20, and 15 feet and the same characteristics were measured in each case. The efficiency factors--propulsive efficiency, nacelle drag efficiency, and net efficiency--were obtained for each wing length by means of force tests and the values are compared to determine the effect of span. Pressure-distribution measurements show the lateral extent of the nacelle interference and the propeller-slipstream effect on the span loading for the various conditions. Complete polar curves and curves showing the variation of nacelle drag with lift coefficient are also included. Force and pressure-distribution tests concur in indicating that, for engineering purposes, the influence of a nacelle and of a propeller, in a usual combination, may be considered to extend laterally on a wing the same maximum distance, or about five nacelle diameters or two propeller diameters outboard of their common axes. All important effects of scale nacelle-propeller combinations may be measured within practical limits of accuracy by tests of a 15-foot-span wing."},
{"title":"The influence of two-dimensional stream shear for airfoil maximum lift.","url":"cran.html#doc484","description":"Vidal, R.J. J. Ae. Scs. 29, 1962, 889. The effects of stream velocity gradients on airfoil maximum lift are defined with experimental data obtained in a simulated two-dimensional slipstream. The experimental results show that when positioned near the slipstream plane of symmetry, the airfoil maximum lift varies markedly with location in the slipstream. In moving the airfoil from above to below the slipstream plane of symmetry through a total distance corresponding to the airfoil thickness, force data and boundary-layer observations show that boundary-layer separation is delayed to higher angles of attack, and the airfoil maximum lift is doubled. It is concluded that the destalling effect observed in the non-uniform slipstream is not associated with slipstream boundary interference, but stems from the influence of the large local slipstream shear on airfoil characteristics. The effects of uniform and nonuniform shear on airfoil lift and pressure distribution are discussed, within the framework of existing first-order, small-shear theory, to show that these effects of shear tend to promote stall. A pohlhausen calculation of the laminar boundary layer in a stream with shear is used to identify and to assess the effects of stream shear on boundary-layer separation criteria. It is demonstrated that these effects are negligibly small, and that the uniform-flow criterion applies. It is concluded on the basis of the experimental data that the observed destalling phenomenon stems from a shear effect of higher order than those treated in the inviscid theories. It is hypothesized that it is a second-order effect, fixed by the product of the stream shear and the derivative of the shear, which was large in the present experiments."},
{"url":"cran.html#doc328","title":"The boundary layer near the stagnation point in hypersonic flow past a sphere.","description":"Herring, T.R. J. Fluid mech. 7, 1960, 257. Flow properties behind shock waves caused by bluff bodies traveling at supersonic speeds are of major importance in missile and high-speed aircraft design. Paper presents a mathematical solution for the laminar boundary layer near the stagnation point of a sphere. Surface temperature is free-stream static and shock is strong. Air is assumed calorically and thermally perfect with a prandtl number of 0.72 and a dynamic viscosity directly proportional to temperature. Based on work of homann (zamm 16, P. 153, 1936) and lighthill simultaneous differential equations for the velocity and temperature profiles. These are solved by numerical integration along a normal to the surface using a digital computer. Results are presented as functions of free-stream mach number, reynolds number, and specific heat ratio. As increases, boundary-layer thickness is shown to decrease while shock stand-off distance increases. Stand-off distance also decreases with increasing and decreasing specific heat. For constant and specific heat ratio, the product of skin-friction coefficient and the square root of decreases with increasing only approaching a constant value at greater than 10, 000. Reviewer's comment is concerned with the perfect gas assumption for air. Author suggests that the effects of dissociation on flow properties are accounted for by a proper choice of specific heat ratio. A consideration of the kinetics of chemical reaction in the cooled boundary layer emphasizes the oversimplification of this approach. The effect on transport properties could have been approximated in present analysis by changing the prandtl number to one more representative of the existing pressures and temperatures."},
{"description":"Coleman, W.S. J. Ae. Scs. 1959, 264. Advances in the practical development of boundary-layer control for the maintenance of extensive laminar flow have drawn attention to the problem of surface roughness, due not only to artificial irregularities such as rivet heads, lap joints, window panels, etc., but also to the kind generated in flight from impact with insects. This natural form of roughening, the effects of which have been noted, though not investigated previously, is the subject of the present paper. The phenomenon may be divided into two parts--namely, and (2) its effect upon the stability of the laminar boundary layer. Wind-tunnel experiments with the fruit fly, drosophila, and the common housefly for the investigation of both (1) and airfoils are fully described. The former problem has also been treated mathematically in a separate paper, not yet published, agreement between theory and experiment being satisfactory in all essentials. The characteristics of the roughness profile consist principally of a pronounced peak near the leading edge, followed by an extensive area of surface over which there is a much reduced and gradually diminishing value of the excrescence height. Further, it is shown that, if the severe leading-edge roughness, or its effect upon the boundary layer, can be eliminated, then the down-stream roughness causes no disturbance to the passage of a laminar layer--I.E., the surface, though roughened, is aerodynamically smooth. Moreover, it appears that the conditions defining the upstream boundary to this region of insignificant roughness are fundamentally the same as those which determine the critical state for transition at an artificial disturbance of a three- dimensional character.","title":"The characteristics of roughness from insects as observed for two-dimensional, incompressible flow past airfoils.","url":"cran.html#doc933"},
{"description":"Bertram, M.H. J.ae.scs. 23, 1956, 898. 85. There is, at present, considerable interest in the characteristies of blunted bodies from both an aerodynamic and a heat-transfer standpoint. The use of blunt shapes is contemplated to reduce the heat-transfer problem at body noses, but there are also applications for blunt noses which occur from mainly aerodynamic considerations. An actual reduction in drag may be the beneficial result of blunting the nose of a cone or a similar slender shape under certain conditions. Although the sphere has received considerable treatment, the nose shapes are not necessarily tangent spheres. In the case, let us say, of a total head tube situated in the nose of a given body, the blunting may be quite flat, and nose sections blunter than spherical shape may conceivably be desirable, in some cases, from the heat- transfer standpoint. The purpose of the present investigation is to examine the aerodynamic effect of a simple type of nose blunting on a basic body. The incompressible flow of an electrically conducting fluid past a porous plate y = 0 with constant suction velocity in the presence of a transverse uniform strength has recently been investigated by gupta. In this note, the problem is generalized to take into account the effect of free convection, when a body force g per unit mass is acting in the negative x-direction parallel to the wall. The fluid is assumed to be semi- incompressible as usual. In addition to the obvious practical significance, this problem is also interesting in the sense that it provides another exact solution of the magnetohydrodynamic equations, since the only electromagnetic assumptions involved are constant properties and freedom from excessive charges.","url":"cran.html#doc44","title":"Tip-bluntness effects on cone pressures at m=6.85."},
{"title":"A simplified method of elastic stability analysis for thin cylindrical shells.","url":"cran.html#doc889","description":"Batdorf, S.B. Naca R.874, 1947. This paper develops a new method for determining the buckling stresses of cylindrical shells under various loading conditions. For convenience of exposition, it is divided into two parts. In part 1, the equation for the equilibrium of cylindrical shells introduced by donnell in naca report no. 479 to find the critical stresses of cylinders in torsion is applied to find critical stresses for cylinders with simply supported edges under other loading conditions. It is shown that by this method solutions may be obtained very easily and the results in each case may be expressed in terms of two nondimensional parameters, one dependent on the critical stress and the other essentially determined by the geometry of the cylinder. The influence of boundary conditions related to edge displacements in the shell median surface is discussed. The accuracy of the solutions found is established by comparing them with previous theoretical solutions and with test results. The solutions to a number of problems concerned with buckling of cylinders with simply supported edges on the basis of a unified viewpoint are presented in a convenient form for practical use. In part 2, a modified form of donnell's equation for the equilibrium of thin cylindrical shells is derived which is equivalent to donnell's equation but has certain advantages in physical interpretation and in ease of solution, particularly in the case of shells having clamped edges. The solution of this modified equation by means of trigonometric series and its application to a number of problems concerned with the shear buckling stresses of cylindrical shells are discussed. The question of implicit boundary conditions also is considered."},
{"description":"Hidalgo, H., taylor, R.L. And Keck, J.C. J. Ae. Scs. 29, 1962. Transition from laminar to turbulent flow in the hypersonic wakes of spheres was detected in laboratory measurements of the radiation from the flow field. A hypervelocity gun facility was used to fire models, 0.22-in. In diameter, into a range at velocities from 10, 000 to 17, 000 ft sec. Experiments were performed by changing.. (a) the material of the projectile ,. (b) the ambient gas in the range ,. And (c) the pressure in the range. Three optical techniques were used to observe the wake radiation.. Which show a turbulent viscous wake as the pressure in the range is decreased from one atmosphere to about 20 cm hg. Which show the luminous flow field at pressures between 30 and ence of short luminous streaks, which disappear suddenly as the pressure is decreased below 3 cm hg for air, and below 0.8 cm hg for argon. Both air and argon, which show the main features of the flow field. Above the transition pressure, the intensity of radiation from the wake is always associated with fluctuations that appear to be the same phenomenon as the drum-camera streaks. The appearance of the streaks in the drum camera and photo-multiplier data is interpreted as transition from laminar to turbulent flow in the viscous wake, because experimental evidence shows that their appearance is not controlled by chemical, radiative, or ablative processes, but depends on aerodynamic effects. This conclusion is supported by other experiments based on optical and schlieren techniques. The transition in the wake at positions very close to the body is given by a local reynolds number of 10 for air, and 3 x 10 for argon. The results indicate a possible local-mach-number effect.","url":"cran.html#doc536","title":"Transition in the viscous wakes of blunt bodies at hypersonic speeds."},
{"title":"Expansions at small reynolds number for the flow past a sphere and a circular cylinder.","url":"cran.html#doc149","description":"Proudman, I. And Pearson, J.R.A. J.fluid mech. 2, 1957, 237. This paper is concerned with the problem of obtaining higher approximations to the flow past a sphere and a circular cylinder than those represented by the well-known solutions of stokes and oseen. Since the perturbation theory arising from the consideration of small non-zero reynolds numbers is a singular one, the problem is largely that of devising suitable techniques for taking this singularity into account when expanding the solution for small reynolds numbers. The technique adopted is as follows. Separate, locally valid the regions close to, and far from, the obstacle. Reasons are presented for believing that these 'stokes' and 'oseen' expansions are, respectively, of the forms where are spherical or cylindrical polar coordinates made dimensionless with the radius of the obstacle, r is the reynolds number, and and vanish with R. Substitution of these expansions in the navier-stokes equation then yields a set of differential equations for the coefficients and, but only one set of physical boundary conditions is applicable to each expansion (the no-slip conditions for the stokes expansion, and the uniform-stream condition for the oseen expansion) so that unique solutions cannot be derived immediately. However, the fact that the two expansions are (in principle) both derived from the same exact solution leads to a 'matching' procedure which yields further boundary conditions for each expansion. It is thus possible to determine alternately successive terms in each expansion. The leading terms of the expansions are shown to be closely related to the original solutions of stokes and oseen, and detailed results for some further terms are obtained."},
{"description":"Lighthill, M.J. J. Fluid mech. 3, 1957, 113. After a brief review of methods of calculating the flow fields produced by disturbances in rotational basic flows, the author points out a fundamental difficulty in the treated as a perturbation of the disturbance field that would occur if the basic flow were uniform).. Slow attenuation of the secondary-flow disturbance with distance from the obstacle. The author conjectured (same J. 1 the trouble was caused by nonuniform validity of the approximation sequence in the region far from the obstacle. The analogy with /stokes' and whitehead's paradoxes/ is mentioned, and a solution analogous to oseen's is suggested, one in which disturbances, but not the shear, are assumed to be small. In this paper, such a solution is found, and is shown to overlap with the small-shear, secondary-flow solution. The basic flow is a parallel, steady, inviscid, two-dimensional shear flow. The / fundamental solution/ due to a weak source is sought. The method of fourier transforms is used. Simple solutions are found for a uniformly sheared basic flow (where the result coincides with the secondary-flow solution) and for an exponential basic-flow profile. In the general case it is assumed that the parallel basic flow becomes uniform at, where the x-axis lies in the flow direction. The character of the solution is determined by studying its hankel transform, especially for the class of flows where the total variation of the basic stream speed v(y) is small. An interpretation in terms of images, due to M. B. Glauert, is given, and finally the relationship of the present work to theories of the displacement of the stagnation streamline (displacement effect of pitot tubes) is discussed.","url":"cran.html#doc660","title":"The fundamental solution for small steady three dimensional disturbances to a two dimensional parallel shear flow."},
{"description":"Halfman, R.L., johnson, H.C. And Haley, S.M. Naca tn.2533, 1951. The problem of stall flutter is approached in two ways. First, using the M.I.T.-naca airfoil oscillator, the aerodynamic reactions on wings oscillating harmonically in pitch and translation in the stall range have been measured, evaluated, and correlated where possible with available published data, with the purpose of providing empirical information where no aerodynamic theory exists. The major effects of reynolds number, airfoil shape, and reduced frequency on the aerodynamic reactions have been reaffirmed. No instances of negative damping were observed in pure translatory motion and the ranges of negative damping occurring in pure pitch had the same general trends noted by other experimenters. Data on the time-average values in the stall range of both lift and moment are presented for the first time. Second, the results of numerous experimental observations of stall flutter have been reviewed and the various known attempts at its prediction have been examined, compared, and extended. The sharp drop in critical speed and change to a predominantly torsional oscillation usually associated with the transition from classical to stall flutter is apparently primarily but not entirely caused by the marked changes in moment due to pitch. Fairly good stall-flutter predictions have been reported only when adequate empirical data for this aerodynamic reaction happened to be available for the desired airfoil shape, reynolds number range, and reduced-frequency range. A semiempirical method of predicting the variations of moment in pitch with airfoil shape, reduced frequency, initial angle of attack, and amplitude of oscillation has been presented.","title":"Evaluation of high angle-of-attack aerodynamic derivative data and stall-flutter prediction techniques.","url":"cran.html#doc441"},
{"description":"During thermal fatigue testing of a specimen with a thin edge, or during rapid temperature changes in the gas flow past turbine blades, the thin edges are deformed plastically in compression during heating and subsequently creep in tension as the bulk of the specimen or blade heats up. The plastic deformation is determined from temperature distributions, which are calculated by biot's variational method. The creep deformation is determined as a function of time by a differential equation, which expresses the balance between increasing elastic stress and reduction of stress due to creep relaxation, and which is solved to a riccati equation soluble in terms of bessel functions, or (iii) by transformation to a second-order differential equation with a periodic coefficient. Using the thermal stresses obtained from the solution of the differential equation, the theoretical thermal fatigue endurance is determined from cyclic (mechanical) stress endurance data. Agreement between theoretical and experimental thermal fatigue endurances is obtained, over ranges of temperature, strain, and strain rate, or equivalently, over ranges of temperature-edge radius and heat transfer coefficient. This agreement supports the use of the theoretical methods in wider contexts. The accuracy of the temperature distributions is better than the accuracy of other factors entering into the correlation between theoretical and experimental endurances. Improvement in the interpretation of experimental results requires consideration of the alteration of the stress cycles during the course of thermal fatigue testing. This requirement is catered for partially by the various solutions of the differential equation for thermal stress.","title":"Mathematical techniques applying to the thermal fatigue behaviour of high temperature alloys.","url":"cran.html#doc767"},
{"url":"cran.html#doc1209","title":"Aerodynamic processes in the downwash-impingement problem.","description":"Vidal, R.J. J. Ae. Scs. 1962. Theoretical and experimental data relating to the downwash impingement problem are examined in order to arrive at a coherent understanding of the process of entrainment of ground particles in the flow. It is demonstrated that a key mechanism in the process is the interaction of nonuniform flow in the ground boundary layer with bluff ground particles. This interaction produces a lift force which, under typical conditions, equals or exceeds the particle weight. In the interest of quantitative prediction of the conditions necessary for particle entrainment, four subsidiary problem areas in the impinging jet are examined. These are the viscous decay, the inviscid flow field, the ground boundary layer, and the forces on a bluff body in nonuniform flow. Applicable theories are used in conjunction with experimental data to assess the accuracy and range of validity of the theories, and to define the stream conditions which will cause particle entrainment. Available data are applied to the establishment of criteria for particle entrainment in the vicinity of the impinging-jet stagnation point. These criteria show that entrainment occurs in a finite annular region on the ground plane, and that the particles most readily entrained are those with a diameter equal to about two-thirds the thickness of the ground boundary layer. The configuration size is shown to influence the process in that the onset of entrainment is fixed by the jet diameter and velocity, and the size of the ground particles. The criteria established provide a quantitative estimate of the conditions causing entrainment and provide a basis for scaling experimental results to a variety of full-scale situations."},
{"title":"Methods for calculating the lift distribution of wings /subsonic lifting surface theory/.","url":"cran.html#doc677","description":"R + m 2884, R.A.E. Rep. Aero. 2353. A.R.C. 13, 439. January 1950. This report contains some fairly simple and economic methods for calculating the load distribution on wings of any plan form based on the conceptions of lifting surface theory. The computer work required is only a small fraction of that of existing methods with comparable accuracy. This is achieved by a very careful choice of the positions of pivotal points, by plotting once for all those parts of the downwash integral which occur frequently and by a consequent application of approximate integration methods similar to those devised by the author for lifting line problems. The basis of the method is to calculate the local lift and pitching moment at a number of chordwise sections from a set of linear equations satisfying the downwash conditions at two pivotal points in each section. Interpolation functions of trigonometrical form are used for spanwise integration both in setting up the downwash equations and in getting the resultant forces on the wing from the local forces. The preliminary chordwise integrations for the downwash are predigested in a series of charts/figs.1-6/,.it is these which make the method a practical computing proposition. The theory is outlined in sections 2-5,.section 6 deals with the solution of the linear equation and section 7 with the resultant forces on the wing. Some examples are worked out in section 8 to compare with other methods,. One solution is given in full detail in tables 8-30 as a guide for computers. Appendices i-vi discuss more carefully some salient points of the mathematical theory, and appendix vii is intended to instruct the computer how to carry out the steps of the calculation."},
{"title":"Real-gas laminar boundary layer skin friction and heat transfer.","url":"cran.html#doc493","description":"Wilson, R.E. J. Ae. Scs. 29, 1962, 640. The laminar-boundary-layer equations have been integrated for the case of a flat plate over a wide range of free-stream enthalpies and velocities and over a wide range of enthalpies of the gas at the wall. The range of free-stream velocities extended up to 25, 000 ft sec at low free-stream enthalpies, corresponding to local conditions on a slender body traveling at high speeds. At low free-stream velocities, the range of free-stream enthalpies extended up to 400, 000 btu slug, corresponding to the local conditions on a blunt body traveling at speeds up to 25, 000 ft sec. The gas was assumed to be in thermodynamic equilibrium at each point in the boundary layer and diffusion effects were neglected. The solutions to the boundary-layer equations were carried out on a high-speed digital computing machine, both skin-friction and heat-transfer coefficients being obtained from the computations. Before presenting the results, the t' method of rubesin and johnson for computing skin-friction coefficients for the perfect-gas case is reviewed. For the real-gas case, the average temperature, t', is replaced by the average enthalpy, h', and the h' method is then used to compute skin-friction coefficients. These values are in excellent agreement with the computing-machine results. It was found that the recovery factor for the real-gas case can be approximated by, the best results for the cases considered being obtained if a value of pr corresponding to the enthalpy, h', is used. Using this recovery factor and reynolds analogy, heat-transfer rates can be computed which, with a few exceptions, are within 5 percent of values obtained from computing-machine results."},
{"description":"Bogdonoff, S.M. And Vas, R.E. J. Ae. Scs. 1961. A series of tests were carried out in the princeton university helium hypersoule wind tunnel on blunt two-dimensional wings at zero angle of attack with sweep angles up to 70 at mach numbers from 7 to 15. The leading edge reynolds number varied from 3, 000 to 25, 000. The measured pressure distributions were compared with the simple summation of the theoretical inviscid effect (based on blast wave theory using the normal mach number) added to the viscous effect (calculated as if no sweep were present). For the unswept wing, the slope of the pressure decay was reasonably well predicted by the theoretical calculations. The viscous theory reasonably predicted the variation in the pressure distribution due to changes in leading-edge reynolds number. By subtracting the theoretical viscous effects, an inviscid mach number dependence of the 2.2 power was found as compared to the value of 2.0 predicted by the inviscid theory. The same approach for the swept wing did not give consistently satisfactory results. Deviations avove and below the calculated value by as much as 40-50 percent were measured and there seemed to be no systematic variation with either mach number or reynolds number. At a constant high reynolds number, it was found that the pressure distribution varied with the distance along the wing with an exponent between about--0.53 and--0.58 except for a rather sharp decrease which occurred for the 70 sweep case. The pressure at a given station for a fixed mach number and given leading edge thickness varied as the cosine of the sweep angle to the 1.1 power as compared to the 1.3 power predicted from general geometrical considerations.","title":"The effect of sweep angle on hypersonic flow over blunt wings.","url":"cran.html#doc1229"},
{"title":"The calculation of aerodynamic loading on surfaces of any shape.","url":"cran.html#doc1342","description":"Falkner, V.M. R + m 1910, august 1943. The object of the report is to establish a routine method for the calculation of aerodynamic loads on wings of arbitrary shape. The method developed is based on potential theory and uses a general mathematical formula for continuous loading on a wing which is equivalent to a double fourier series with unknown coefficients. In order to evaluate the unknown coefficients the continuous loading is split up into a regular pattern of horseshoe vortices, the strengths of which are proportional to the unknown coefficients and to standard factors which are given in a table. The total downwash at chosen pivotal points is obtained by summing the downwashes due to the individual vortices, a process which is simplified by the use of specially prepared tables of the properties of the horseshoe vortex. By equating the downwash to the slope of the wing at each pivotal point, simultaneous equations are obtained, the solution of which defines the unknown coefficients. The first layout involves a total of 76 vortices over the wing, and a second layout, involving a total of 84, is shown to be of superior accuracy. The effect on the solution of the number of pivotal points is investigated and it is concluded that by a suitable choice, it is unnecessary to use a large number. Results for a rectangular wing at with those obtained by other workers and it appears that there may be errors in published results in at least one of these cases. Immediate development includes the application to the calculation of the characteristics of actual sweptback wings, including rotary derivatives, and future development includes also applications in wind tunnel design and technique."},
{"url":"cran.html#doc1300","title":"Some effects of bluntness on boundary layer transition and heat transfer at supersonic speeds.","description":"Moeckel, W.E. Naca R.1312, 1957. Large downstream movements of transition observed when the leading edge of a hollow cylinder or a flat plate is slightly blunted are explained in terms of the reduction in reynolds number at the outer edge of the boundary layer due to the detached shock wave. The magnitude of this reduction is computed for cones and wedges for mach numbers to 20. Concurrent changes in outer-edge mach number and temperature occur in the direction that would increase the stability of the laminar boundary layer. The hypothesis is made that transition reynolds number is substantially unchanged when a sharp leading edge or tip is blunted. This hypothesis leads to the conclusion that the downstream movement of transition is inversely proportional to the ratio of surface reynolds number with blunted tip or leading edge to surface reynolds number with sharp tip or leading edge. This conclusion is in good agreement with the hollow-cylinder result at mach 3.1. Application of this hypothesis to other mach numbers yields the result that blunting the tip of a slender cone or the leading edge of a thin wedge should produce downstream movements of transition by factors ranging from 2 at mach 3.0 to 30 at mach the possible reduction in over-all heat-transfer rate and friction drag for aircraft flying at high supersonic speeds. Mach number profiles near the surfaces of blunted cones and wedges are computed for an assumed shape of the detached shock wave at flight mach numbers to 20. The dissipation and stability of these profiles are discussed, and a method is described for estimating the amount of blunting required to produce the maximum possible downstream movement of transition."},
{"description":"Galletly, G.D. J. Eng. For industry, 1959, 51. It has recently become apparent, through a rigorous stress analysis of a specific case that designing torispherical shells by the current edition of the asme code on unfired pressure vessels can lead to failure during proof-testing of the vessel. The purpose of the present paper is to show in what respects the code fails to give accurate results. As an illustrative example, a hypothetical pressure vessel with a torispherical head having a diameter-thickness ratio of 440 was selected. The supports of the vessel were considered to be either on the main cylinder or around the torus. The vessel was subjected to internal pressure and the elastic stresses in it were determined rigorously and by the code. A comparison of the two revealed that the code predicted stresses in the head which were less than one half of those actually occurring. Furthermore, the code gave no indication of the presence of high compressive circumferential direct stresses which exceeded 30, 000 psi for practically the entire torus. If the head had been fabricated using a steel with a yield point of would have failed or undergone large deformations, whereas the code would have predicted that it was safe. The code's rules for torispherical heads are thus in need of revision for certain geometries. The implications of the foregoing results are currently being studied by the asme,. In the interim, however, designers should exercise care in applying the code to torispherical shells. It is also shown in the paper that the use of the membrane state as a particular solution of the differential equations is not a good approximation for toroidal shells of the type considered.","title":"Torispherical shells - a caution to designers.","url":"cran.html#doc1134"},
{"description":"Tani, I. J.phys.soc.japan, 4, 1949, 149. The theory of the laminar boundary layer offers a means of determining the skin friction under the assumption of a given velocity distribution outside the boundary layer. Owing to the mathematical difficulties, however, exact solutions are possible only when the velocity distribution is expressed as a simple function of the distance along the surface. More complicated velocity distributions necessitate recourse to the method of expansion in series or that of step-by-step calculations, but the labor involved is too great for the methods to be of practical use. Approximate method due to pohlhausen (1921), which had long been recommended for general use, gives a reasonably accurate solution in a region of accelerated flow, but recently its adequacy in a region of retarded flow has been questioned. Separation of flow may actually occur where the solution of pohlhausen fails to give it. More recently howarth solution, which gives fairly reasonable results in a region of retarded flow. Howarth's solution essentially consists in solving the boundary layer equations for the particular case in which the velocity u outside the boundary layer decreases linearly with the distance x measured along the surface, and utilizing the solution by replacing the actual distribution of u by a circumscribing polygon of infinitesimal sides. Therefore, it is assumed that the velocity distribution at any section depends on the velocity gradient du/dx at that section only, being affected by the conditions upstream only in so far as this affects the momentum thickness 0. In other words, the velocity distribution across the boundary layer is determined by a parameter.","title":"On the solution of the laminar boundary layer equations.","url":"cran.html#doc459"},
{"title":"The law of the wake in the turbulent boundary layer.","url":"cran.html#doc563","description":"Coles, D. J. Fluid mech. 1, 1956, 191. After an extensive survey of mean-velocity profile measurements in various two-dimensional incompressible turbulent boundary-layer flows, it is proposed to represent the profile by a linear combination of two universal functions. One is the well-known law of the wall. The other, called the law of the wake, is characterized by the profile at a point of separation or reattachment. These functions are considered to be established empirically, by a study of the mean-velocity profile, without reference to any hypothetical mechanism of turbulence. Using the resulting complete analytic representation for the mean-velocity field, the shearing-stress field for several flows is computed from the boundary-layer equations and compared with experimental data. The development of a turbulent boundary layer is ultimately interpreted in terms of an equivalent wake profile, which supposedly represents the large-eddy structure and is a consequence of the constraint provided by inertia. This equivalent wake profile is modified by the presence of a wall, at which a further constraint is provided by viscosity. The wall constraint, although it penetrates the entire boundary layer, is manifested chiefly in the sublayer flow and in the logarithmic profile near the wall. Finally, it is suggested that yawed or three-dimensional flows may be usefully represented by the same two universal functions, considered as vector rather than scalar quantities. If the wall component is defined to be in the direction of the surface shearing stress, then the wake component, at least in the few cases studied, is found to be very nearly parallel to the gradient of the pressure."},
{"title":"High-speed viscous corner flow.","url":"cran.html#doc1250","description":"Bloom, M.H. And Rubin, S. J. Ae. Scs. 1961, 145. A boundary-layer integral method analysis is set up for compressible laminar flow in a symmetric corner with varying angle and streamwise pressure gradient. It represents an extension and modification of the constant density analysis of loitsianskii and bolshakov. The analysis is applied to the case of constant pressure, constant corner angle, and isothermal surfaces, for which the crocco velocity-enthalpy relation holds. Although simplifying assumptions limit the quantitative accuracy outside the 60 to 120 angle range, some qualitative trends are probably correct outside this range. The limiting cases near 0 and 180 are not considered. Favorable agreement between some results obtained by the integral method and by other methods is demonstrated for the isothermal, constant-density case. Results show an increasingly sharp merger of the outermost isovels of streamwise velocity as the mach number increases. This sharp merging of the outer isovels is increased by increasing corner angle and by insulation of heating of the surfaces. Within the interior of the viscous layer the spreading or contraction of the disturbed region of merging is influenced by surface heat-transfer conditions. Surface shear and heat flux are decreased in the disturbed region, and are zero at the apex. For cases corresponding roughly to the higher mach numbers of wider corner angles, the /specific momentum-area/ exhibits the same decrease with mach number as its two-dimensional counterpart, whereas the /specific displacement-area, / a measure of stream-tube dilation, increases more rapidly with mach number than the comparable two-dimensional parameter."},
{"url":"cran.html#doc24","title":"Theory of stagnation point heat transfer in dissociated air.","description":"Fay, J.A. And Riddell, F.R. J. Ae. Scs. 25, 1958, 73. The boundary-layer equations are developed in general for the case of very high speed flight where the external flow is in a dissociated state. In particular the effects of diffusion and of atom recombination in the boundary layer are included. It is shown that at the stagnation point the equations can be reduced exactly to a set of nonlinear ordinary differential equations even when the chemical reactions proceed so slowly that the boundary layer is not in thermochemical equilibrium. Two methods of numerical solution of these stagnation point equations are presented, one for the equilibrium case and the other for the nonequilibrium case. Numerical results are correlated in terms of the parameters entering the numerical formulation so as not to depend critically on the physical assumptions made. For the nonequilibrium boundary layer, both catalytic (to atom recombination) and noncatalytic wall surfaces are considered. A solution is represented which shows the transition from the /frozen/ boundary layer (very slow recombination rates) to the equilibrium boundary layer (fast recombination rates). A recombination rate parameter is introduced to interpret the nonequilibrium results, and it is shown that a scale factor is involved in relating the equilibrium state of a boundary layer on bodies of different sizes. It is concluded that the heat transfer through the equilibrium stagnation point boundary layer can be computed accurately by a simple correlation formula and that the heat transfer is almost unaffected by a nonequilibrium state of the boundary layer provided the wall is catalytic and the lewis number near unity."},
{"description":"Uram, E.M. J. Ae. Scs. 1960, 659. A new method of calculating the behavior of turbulent boundary layers in adverse pressure distributions is developed which permits direct determination of the velocity profile rather than the gross integral parameters normally used to infer the general character of the boundary layer. The method offers the simplicity of algebraic equations coupled with the use of charts rather than the laborious simultaneous solution of coupled differential equations required by existing methods. The method also affords, for the first time, a means of determining the total boundary-layer thickness, thus allowing calculation of the absolute as well as the nondimensional velocity distribution. The velocity profile is considered to be composed of two regions--an inner region which is described by the law of the wall and an outer region which is described by a function depicting the deviation from that law. The deviation function involves two parameters which are uniquely dependent upon the skin-friction coefficient and a third parameter which, for practical purposes, can be considered a constant. Since the entire velocity distribution was found to be almost uniquely dependent upon the local skin friction, serious doubt is cast upon the generally accepted /history concept/ which considers the outer region of the boundary layer to be dependent on integrated upstream conditions. Agreement between experimental velocity distributions and those calculated by the method presented here is generally very good. The analysis and calculation procedures which are presented are applicable to two-dimensional, pseudo-two- dimensional, and axisymmetric conical flows.","url":"cran.html#doc1261","title":"A method of calculating velocity distribution for turbulent boundary layers in adverse pressure distributions."},
{"url":"cran.html#doc304","title":"First-order approach to a strong interaction problem in hypersonic flow over an insulated flat plate.","description":"Oguchi, H. Univ. Tokyo aero.res r330, 1958. The present paper concerns with the strong interaction phenomenon over an insulated semi-infinite flat plate with a sharp leading edge. In particular the main interest is in the consistent treatment in which the boundary-layer solution may be joined continuously with the inviscid solution regarding flow variables including pressure, normal velocity, temperature (or streamwise velocity) and density. It is shown that the behavior of the inviscid solution may be consistent with that of the boundary-layer solution to at least first-order approximation that is correct to the order of, where m is the mach number of undisturbed flow, r the reynolds number based on the distance from leading edge and the ratio of specific heats. Then the first-order boundary-layer problem is formulated under such an external circumstance and an attempt is made for arriving at the solution. Actual calculations are carried out for both cases of air and helium. From the solution it is found that the region in which the viscous effect plays a significant role is ranged over from 0 to a certain finite value of n, say n, in terms of the similarity coordinate n in the corresponding incompressible boundary layer. The numerical results moreover indicate that the induced pressure is considerably smaller than the estimate of lees (7) obtained by his approximate method in which the effect of the first-order induced pressure on the boundary layer is ignored and no survey of the first-order boundary-layer equation is made. The present results are also found to be in excellent agreement with experimental data recently obtained in helium flow by erickson (15)."},
{"url":"cran.html#doc1351","title":"Exploratory tests of the effects of jet plumes on the flow over cone- cylinder flare bodies.","description":"Falanga, R.A. Nasa tn.d1000, 1962. Schlieren photographs have been taken of the flow over cone-cylinder-flare bodies to study the extent of boundary-layer separation due to the presence of rocket jet plumes. Tests were made of three cone-cylinder-flare configurations in the langley 11-inch hypersonic tunnel at a mach number of 9.65 and in the langley unitary plan wind tunnel at a mach number of 4.65 with two additional configurations. The stream reynolds number varied from approximately 317, 000 to 582, 000 based on model length. The conical flares had half-angles of 7 or 13 and contained one of two test nozzles with a design mach number of 3.72 or 4.53. The test nozzles were operated with compressed air and were designed to simulate a solid-propellant rocket motor operating at altitudes between to free-stream static-pressure ratio varied from jet off to 1, 150 for the test nozzle with a design mach number of 3.72 and from jet off to mach number of 4.53. For most of the tests the angle-of-attack range was 0 to -4,. Some additional tests were made at 2 and 4. Measurements taken from flow pictures indicated that at zero angle of attack on all configurations tested with jet on the boundary layer separates ahead of the flare-cylinder juncture and the separation point moves toward the cone-cylinder juncture with an increase in pressure ratio. Increasing angle of attack reduced the extent of boundary-layer separation on the windward side as did increasing the stream mach number from 4.65 to 9.65. Other parameters which tended to reduce the extent of boundary-layer separation were.. Number, (b) decreasing stream reynolds number, and (c) displacing nozzle exit rearward."},
{"description":"Kilakowski, L.J. And Haskell, R.N. J. Ae. Scs. 1961. The method proposed in this paper is based on an approximate solution of the integral equation which represents the potential flow about a finite wing, with no restrictions beyond those necessary for linearization. After assuming the usual series representation of the wing surface vorticity distribution, the solution is achieved by approximating portions of the kernels of the transformed integral equation by single and double fourier series and performing termwise integrations analytically. This is followed by the routine inversion of the aerodynamic influence coefficient matrix, after satisfying appropriate boundary conditions at selected control points. In this procedure the number of control point used is limited only by the storage capacity of the computer. Control points may be located so as to cover the entire wing surface, with due regard to certain physical requirements, permitting the accurate representation of complicated mean surface shapes. An evaluation of the proposed method is included. Comparisons with other theoretical methods and electrical analogy tank results are used to substantiate the accuracy of the proposed method when applied to plane wings. A final evaluation involves a comparison of calculated surface pressure distribution with wind-tunnel measurements on a swept, tapered wing with a cambered and twisted mean surface. The agreement evidenced in the latter comparison has the same order of overall accuracy as similar comparisons on plane wing planforms. In either case, the results given by the proposed method are within the accuracy requirements for most aircraft design studies.","url":"cran.html#doc1246","title":"Solution of subsonic nonplanar lifting surface problems by means of high-speed digital computers."},
{"description":"Benjamin, T.B. J. Fluid mech. Vol. 9, 4, 1960. P513. Purpose of paper is to examine theoretically the use of coatings of elastic materials to prevent transition from laminar to turbulent flow. Theory is extension to flexible boundary of the small-disturbance tollmien-schlichting stability theory and makes use of /tietjens function/ and other functions that occur in solution of orr-sommerfeld equation. It is shown how solutions for flexible wall can be obtained from solutions for rigid boundary. Outline and discussion is given first for tollmien-schlichting stability theory for rigid wall, then for theory for flexible boundary. Theory is given both for a nondissipative and a dissipative flexible boundary. Behavior of flexible medium itself is also examined. Practical requirements are discussed. For example, a conclusion is that to avoid tollmien-schlichting instability, the wave velocity of surface waves in absence of flow should coincide with tollmien-schlichting wave velocity at wavelength of /most dangerous/ tollmien-schlichting waves. Moreover, damping should be large enough to prevent surface waves from developing but not so large that tollmien-schlichting waves are permissable. Author states that a boundary that is both soft and light, one whose elastic constants are of same order as the dynamic pressure of the flow, may be practical for use at high speeds. This surface should have a small damping to avoid tollmien-schlichting type of instability and a large enough wave speed without flow to avoid surface wave instability. Although paper is somewhat sketchy in places, it gives comprehensive coverage of stability of laminar flow over a flexible wall.","url":"cran.html#doc1321","title":"Effects of a flexible boundary on hydrodynamic stability."},
{"description":"Woods, L.C. Arc cp115, 1953. This paper sets out the method now used by the author of applying the polygon method to the calculation of the compressible subsonic flow round two-dimensional aerofoils. Tables have been constructed which can be used for all aerofoil shapes, putting the polygon method on the same footing numerically as goldstein's method has the advantage over approximation 3 that it can be applied in the following cases which are beyond the scope of goldstein's method.. Conventional aerofoils, (b) the low-speed flow about very thick aerofoils, E.G., in reference 3 it is applied to circular cylinders, (c) the flow about symmetric aerofoils between either straight or constant pressure walls, (d) flow in asymmetric channels, and (e) more difficult problems of the flow about aerofoils in the presence of one or two constraining walls (to be published). A method of calculating lift and moment coefficients, and their rates of change with incidence (a) is also given in the paper. As an example the velocity distribution and the rates of change of the lift and moment coefficients with a are calculated for the aerofoil R.A.E.104 at values of m (mach number at infinity) of 0, and 0.7, for various values of the incidence, A. The velocity distributions for zero incidence are found to be in fair agreement with the corresponding experimental results. The results at incidence are in satisfactory agreement with the experimental results, not for the same incidence, but for the same lift coefficient. It is found, for example, that at m = 0.7 the theory for a = 0.8 agrees best with experiment for a = 1.0, when the lift coefficients are approximately the same.","url":"cran.html#doc206","title":"The applications of the polygon method to the calculation of the compressible subsonic flow round two-dimensional profiles."},
{"description":"Levy, L.L. Nasa tn.d1427, 1962. An analysis has been made of atmosphere entries for which the spacecraft lift-drag ratios were modulated to limit the maximum deceleration. The parts of the drag polars used during modulation were from maximum lift coefficient to minimum drag coefficient. Five drag polars of different shapes were assumed for the spacecraft. The entries covered wide ranges of initial velocity, initial flight-path angle, initial and maximum lift-drag ratio. Two-dimensional trajectory calculations were made for a nonrotating, spherical earth with an exponential atmosphere. The results of the analysis indicate for four of the five drag polars that, relative to the maximum deceleration of an unmodulated entry at maximum lift-drag ratio, the greatest reduction in maximum deceleration obtainable by modulation depends upon a single parameter. This parameter is the ratio of the value of the aerodynamic resultant-force coefficient at minimum drag coefficient to the value at maximum lift coefficient. Thus, the reduction in maximum deceleration is independent of initial velocity, initial flight-path angle, initial maximum lift-drag ratio, and the shape of the drag polar. For the fifth drag polar, the reduction in maximum deceleration was found to depend upon the maximum lift-drag ratio. Also, relative to the depth of a given deceleration-limited corridor, the greatest increase in corridor depth obtainable by modulation (for four of the five drag polars) depends upon the same ratio of aerodynamic resultant-force coefficients. The fractional increase in corridor depth can be expressed as an empirically determined analytical function of this ratio.","title":"Atmosphere entries with spacecraft lift-drag ratios modulated to limit decelerations.","url":"cran.html#doc1291"},
{"description":"Crewe, P.R. And Eggington, W.J. Trans. Roy. Inst. Naval arch. 1960. The hovercraft is the first operational british project in the ground-effect machine field. Although there has, for a number of years, been a tentative searching after the principles underlying such machines, it is only now that their possibilities as commercial transport and service craft are beginning to be developed. Since the hovercraft is a new vehicle, the appearance of the saunders-roe sr-n1, a manned experimental craft, excited considerable public attention and there have been a number of descriptive articles in the press. Papers of a more technical type, on ground-effect machines, are now beginning to appear and it is to be expected that these will rapidly increase in number, especially since american interest in both the commercial and defence fields is expanding fast. The authors of the present paper have, therefore, concentrated attention upon features about which they had something personal to say, and which they consider to be of particular significance for assessing the possibility of the hovercraft becoming important in maritime transport. These features are..- the hovercraft as a fundamentally new principle in the transport field. The powering requirements and resistance characteristics. The likely operating costs of hovercraft in comparison with other forms of maritime transport. In addition, relatively brief descriptions of the history and the current work being undertaken on the ground-effect machine and of the design, construction, and testing of the saunders-roe sr-n1 are provided. The final section discusses outstanding problems and some future possibilities.","title":"The hovercraft - a new concept in maritime transport.","url":"cran.html#doc649"},
{"url":"cran.html#doc294","title":"An investigation of laminar transitional and turbulent heat transfer on blunt-nosed bodies in hypersonic flow.","description":"Cresci, R.J. And Mackenzie, D.A. J. Ae. Scs. 27, 1960. Laminar, transitional, and turbulent heating rates have been measured by means of the shrouded model technique. The reynolds number was varied over a ninefold range,. The enthalpy ratio (stagnation to wall) varied from 2.3 to approximately 1.5. Two different pressure distributions were imposed on the model which consisted of a spherically capped cone. The experimental data are compared to the laminar hypersonic boundary-layer theory and shown to be in good agreement on the conical portion of the model. On the spherical portion the data are approximately 20 per cent higher than the theoretical prediction. Some of this discrepancy can be attributed to radiation to the nose of the model. The fully developed turbulent heat-transfer data are compared to two theories.. (1) a relatively simple turbulent theory which is based on recent theoretical work and which takes into account the upstream history of the boundary layer, and (2) the flat-plate reference-enthalpy theory, which depends on only /local/ conditions. Although both theories are in reasonable agreement with the data, the latter method is simpler and somewhat more accurate. For transitional flow the theory mentioned first can be readily modified in order to permit reasonable estimates of transitional heat transfer to be obtained. On this basis it is possible to estimate laminar, transitional, and fully developed turbulent heat transfer under hypersonic blunt-body conditions. The behavior of transition reynolds number based on momentum thickness is also discussed and shown to be in quantitative agreement with recent shock-tube measurements."},
{"title":"The performance of supersonic turbine nozzles.","url":"cran.html#doc213","description":"Stratford, B.S. And Sansome, G.E. Arc r + m 3273, 1959. An investigation has been conducted at the national gas turbine establishment into the performance of turbines having high pressure ratios per stage. The present report discusses the mode of operation of supersonic nozzles for such turbines, and describes a cascade experiment. Both theory and experiment demonstrate that the conditions imposed upon the supersonic flow immediately downstream of the nozzles (E.G., by a following row of rotor blades) exert an overriding influence upon the nozzle outlet flow angle, and hence upon the maximum pressure ratio obtainable across the nozzle--providing that the axial component of velocity is subsonic. This is an important difference from the more familiar flow of subsonic turbine nozzles, where, for example, the downstream gas angle is controlled predominantly by the nozzle blade shape and spacing. A suitable test technique using a closed-jet tunnel is demonstrated. The particular nozzles tested, of convergent-divergent form, had a straight-sided divergent portion of to axial direction) and a design mach number of 2. The flow was found to be well behaved as regards shock pattern, losses, and starting over the range of pressure ratios tested--between 9 1 and 19 1. In particular the efficiency at the design pressure ratio of 16.6 1 was high, the velocity coefficient calculated from traverses of pitot and static tubes being 0.98. For the conversion of pitot to total pressure at a mach number of 2.5 a high accuracy is important in the measurement of the static pressure,. Nevertheless readings from a conventional four-hole instrument appear to be reliable."},
{"title":"Experiments with a tapered swept-back wing of warren 12 planform at mach numbers between 0.6 and 1.6.","url":"cran.html#doc794","description":"Hall, I.M. And Rogers, E.W.E. A.R.C. R + m 3271, part ii, july 1960. 6 and 1.6. The development of the flow pattern on a wing of aspect ratio 2 828, taper ratio 0 333, leading-edge sweepback 53 5 deg and 6 per cent thickness/chord ratio in the streamwise direction has been described in part 1, which discussed oil-flow patterns obtained on the surface of the wing. The complete programme of tests also included pressure plotting at four spanwise stations and force measurements. These are discussed in relation to the flow development in this part of the report. The wing was tested at mach numbers between 0 6 and 1 6 for incidences up to about 14 deg. The tunnel stagnation pressure was held constant at a value near atmospheric pressure during the tests, so that the reynolds number varied with mach number.. At m 1 0 it was 2 3 x 10 based on the mean aerodynamic chord. Boundary-layer transition was fixed by a roughness band at the leading edge. A detailed analysis has been made of the pressure distributions on the surface of the wing and the chordwise distributions integrated to determine the spanwise loading. The overall lift and pitching moment of the wing were also obtained from these data, as well as from direct measurements using a strain-gauge balance, by means of which the wing drag was also determined. These results are considered in some detail to illustrate the effects of mach number and incidence on the flow about the model. A preliminary analysis is also made of the conditions for boundary-layer separation due to shock waves on the wing surface. The principal factor appears to be the component of mach number normal to the shock front."},
{"url":"cran.html#doc820","title":"Theories of plastic buckling.","description":"Batdorf, S.B. J. Ae. Scs. 16, 1949, 405. The theory for the plastic buckling of columns which appears finally to have achieved a satisfactory form, rests upon the well-established uniaxial stress-strain relation. The development of a correspondingly satisfactory theory for the plastic buckling of plates has been hampered by the nonexistence of an established polyaxial stress-strain relation in the plastic range. Present theories for the polyaxial stress-strain relation beyond the elastic range can be divided into two types, often called flow and deformation theories. Theories of plastic buckling based on deformation theories are in better agreement with experiment than those based on flow theories. On the other hand, tests in which a material is compressed into the plastic range and then subjected to shear at constant compressive stress are in better agreement with flow than with deformation theories. Legitimate doubt therefore has existed as to the validity of any theory for the plastic buckling of plates. As a result of studying these apparent contradictions, a new theory of plasticity has been developed which is of neither the flow nor the deformation type. It is based upon the concept of slip, and its formulation was guided more by physical, and less by mathematical, considerations than previous theories. Experimental evidence of limited scope but of crucial character is in better agreement with the new theory than with either flow or deformation theories. The new theory accounts for the apparent contradictions previously alluded to and justifies the use of deformation theory in the analysis of the plastic buckling of plates."},
{"description":"Mirels, H. Naca tn.3712, 1956. The boundary layer behind a shock or thin expansion wave advancing into a stationary fluid has been determined. Laminar and turbulent boundary layers were considered. The wall surface temperature behind the wave was also investigated. The assumption of a thin expansion wave is valid for weak expansions but becomes progressively less accurate for strong expansion waves. The laminar-boundary-layer problem was solved by numerical integration except for the weak wave case, which can be solved analytically. Integral (karman-pohlhausen type) solutions were also obtained to provide a guide for determining expressions which accurately represent the numerical data. Analytical expressions for various boundary-layer parameters are presented which agree with the numerical integrations within 1 percent. The turbulent-boundary-layer problem was solved using integral methods similar to those employed for the solution of turbulent compressible flow over a semi-infinite flat plate. The fluid velocity, relative to the wall, was assumed to have a seventh-power profile. The blasius equation, relating turbulent skin friction and boundary-layer thickness, was utilized in a form which accounted for compressibility. Consideration of the heat transfer to the wall permitted the wall surface temperature, behind the wave, to be determined. The wall thickness was assumed to be greater than the wall thermal-boundary-layer thickness. It was found that the wall temperature was uniform (as a function of distance behind the wave) for the laminar-boundary-layer case but varied with distance for the turbulent-boundary-layer case.","title":"Boundary layer behind shock or thin expansion wave moving into stationary fluid.","url":"cran.html#doc72"},
{"description":"Smith, A.M.O. And Clutter, D.W. J. Aero. Sc. April, 1959. P.229-245, 256. An investigation was made to determine the smallest size of isolated roughness that will affect transition in a laminar-boundary layer. Critical heights for three types of roughness were found in a low-speed wind tunnel. The types were /1/ two-dimensional spanwise wires, /2/ three-dimensional discs, and /3/ a sandpaper type. In addition to type of roughness, test variables included the location of roughness, pressure distribution, degree of tunnel turbulence, and length of natural laminar flow. The most satisfactory correlation parameter was found to be the roughness reynolds number, based on the height of roughness and flow properties at this height. The value of this critical reynolds number was found to be substantially independent of all test variables except the shape of roughness. This parameter also correlates well other published data on critical roughness in low-speed flow. The value of the roughness reynolds number necessary to move transition forward to the roughness itself was also determined for the three types of roughness and was found to be approximately constant for a given type of roughness. An investigation of the limited amount of available data on critical roughness in supersonic flow indicates that the effects of roughness may still be correlated by the roughness reynolds number. The value of this reynolds number depends primarily on the mach number at the top of the roughness. When this mach number is greater than 1.0, the roughness reynolds number based on conditions behind a shock is probably the characteristic parameter.","title":"The smallest height of roughness capable of affecting boundary-layer transition.","url":"cran.html#doc710"},
{"url":"cran.html#doc416","title":"Methods of boundary-layer control for postponing and alleviating buffeting and other effects of shock-induced separation.","description":"Pearcey, H.H. And Stuart, C.M. Smf fund paper, no. F.F. -dash 22, 1959. The use of boundary-layer control to increase the separation-free margins of mach number and lift coefficient beyond the cruise point of high-speed aircraft may often be preferred to design changes that impair the cruising performance or the landing and take-off characteristics. The factors that influence the choice of method and details of its application are discussed, emphasising particularly the need to maintain effectiveness over most of the chord to cover the wide range of separation positions encountered as the shock moves over the wing with changing flight conditions. Research at the national physical laboratory that has embraced high-velocity blowing, vane and air-jet vortex generators, and, in a preliminary way, distributed suction, is briefly described. The relative merits of the various methods are discussed, and some results achieved in their application are given. For vortex generators, the importance is stressed of the vortex paths determined by the interactions of neighbouring vortices and their images. Thus, systems of counter-rotating vortices always leave the surface in pairs and lose their effectiveness. Co-rotating systems are therefore preferred for many applications. Blowing, which in wind-tunnel tests gives results as good as or better than vortex generators and does not have the disadvantage of a drag penalty at cruise, has not yet been assessed in flight. Air-jet vortex generators, which would also avoid the drag penalty, show promise of producing significant effects with relatively small blowing pressures and quantities."},
{"description":"Garner, H.C. And Walshe, D.E. A.R.C. 20, 982, r + m 3244. May 1959. Extensive tables are given of pressure coefficients measured at reynolds numbers from 1.3x10 to 3.9x10 on two half-models of identical planform with 5( rae 101 and 9( rae 101 streamwise sections. The planform of aspect ratio 3.899 has a straight trailing edge with 60degree of sweepback, constant chord over most of the span and a parabolic outer portion of the leading edge curving to a pointed tip. The overall wing characteristics are obtained from integrated normal pressures and are compared with lifting-surface theory. The low-speed experimental pressure distributions and surface oil-flow patterns are analysed and discussed in relation to the onset of separation and the distinct vortex flows that develop at high incidence. Series of contrasting upper-surface isobars illustrate some features of the different stalling processes of the two wings. The direct influence of the main vortex on local surface pressures is assessed in general terms. A fuller appraisal of secondary surface flow is obtained from the oil patterns, observations in water and measurements of high suction near the trailing edge. Studies of the extent of leading-edge stall and location of part-span vortices, in particular two simultaneous leading-edge vortices on the thinner wing, follow from further analysis of local surface pressures. After a detailed discussion of the effect of reynolds number and the distinct types of separated flow, a few results with leading-edge roughness are considered in relation to scale effect on separation and the extensive influence of part-span roughness.","title":"Pressure distribution and surface flow on 5( and 9( thick wings with curved tip and 60degree sweepback.","url":"cran.html#doc675"},
{"description":"Schaffer, A. J. Ae. Scs. 1960, 193. The cancellation of a vortex by means of another concentric vortex of equal strength but opposite spin is investigated. When such a cancellation occurs, there is a recovery of static pressure. The vortices are generated by means of two three-dimensional airfoils cantilevered from the duct wall, one being situated in the wake of the other. The airfoils have opposite effective angles of attack and therefore have trailing vortices of opposite spin, as required. It is demonstrated experimentally that there exists an optimum angle of attack for the second airfoil which cancels the vortex from the first airfoil and restores uniform flow downstream of the two airfoils. A theoretical solution of this optimum angle of attack is presented, and it is found to depend upon the angle of attack of the first airfoil and upon the geometrical properties of the wings. The pressure recovery accompanying the vortex cancellation is also studied. Theoretical considerations, based on the model of a vortex filament in the center of a circular tube show that a maximum of 62 per cent of the static pressure drop across the first airfoil can be recovered. This maximum is imposed, irrespective of skin friction and separation losses, by the irreversibility associated with establishing a vortex field. Experimental pressure recoveries of 50 per cent are realized. Perhaps the primary value of the present study is the opportunity it provides to verify certain of the fundamental concepts of fluid mechanics which are brought into play when the trailing vortex system of a lifting wing is cancelled by a second wing.","url":"cran.html#doc1277","title":"A study of vortex cancellation."},
{"description":"Oguchi, H. Aiaa jnl. U, 1963, 361. The present paper is mainly concerned with the hypersonic flow over a flat plate with a blunt nose. The analysis is based on the flow model in which the flow field behind the shock wave may be divided into two regions.. The inviscid-hypersonic-flow region and the entropy layer, across which the pressure has no appreciable change. The equations for the entropy layer can be reduced to those of the usual boundary-layer problem with the exception that the outer edge of the entropy layer, as well as the pressure remain unknown. These unknowns are determined so as to approximately match the entropy-layer solution with the inviscid hypersonic solution in which the shock wave has the shape of the power law of the distance from the leading edge. The assumed flow model is shown to be valid over a restricted range depending on the wall-to-stagnation temperature ratio and (where is the reynolds number based on half the thickness of nose t, m the freestream mach number, and c the chapman-rubesin constant. Actual calculations have been carried out for the case with typical values of and the wall-to-stagnation temperature ratio. The calculated values for both the surface pressure and heat-transfer rate are compared with the experimental data. As regards surface pressure in particular, a satisfactory agreement with the data is obtained. The validity of the assumptions upon which the present analysis is based has been examined from the numerical results, and the region of the validity has been found to extend over a certain large range of the nondimensional distance from the leading edge.","url":"cran.html#doc1198","title":"The blunt-leading-edge problem in hypersonic flow."},
{"url":"cran.html#doc1381","title":"Effect of mach number on boundary layer transition in the presence of pressure rise and surface roughness on an ogive-cylinder body with cold wall conditions.","description":"Carros, R.J. Naca rm a56b15, 1956. The effect of mach number variation from 1.8 to 7.4 on boundary-layer transition was investigated on a slender fin-stabilized ogive-cylinder body in free flight at a constant length reynolds number of 13.8 million. The wall to free-stream temperature ratio was constant at a value of 1.0 below mach number 4.5 and at a value of of the test showed that increasing mach number had a very favorable effect of increasing the extent of the laminar boundary layer for a given surface roughness. The transition data, when plotted as a function of a factor indicative of heat transfer, showed that heat transfer was possibly responsible for a good deal of the increase in transition reynolds number with mach number. Transition was found to occur farther forward on the sheltered side of the body than on the windward side for angles of attack as low as 0.4 and for all mach numbers. The pressure rise along sheltered-side stream-lines was examined and it was found that the pressure-rise coefficient at the transition point, showed no variation with mach number. Data from other sources for different test conditions, when reduced to values of pressure-rise coefficient, were also found to correlate well with that of the present investigation with the exception of data at low subsonic mach numbers. These present results also show that mach number, surface roughness, pressure rise, and length reynolds number all affected boundary-layer transition in the region of theoretical infinite laminar stability to small two-dimensional disturbances as calculated for a flat plate with zero pressure gradient."},
{"description":"L. E. Goodman and J. V. Rattayya University of minnesota, minneapolis, minnesota. Panel flutter. With the development of high-speed aircraft and missiles, vibration of panels has become a problem of practical significance. Many of the failures of the early german rockets after attaining supersonic speed have been attributed to the development of such panel oscillations. It appears this phenomenon is not of much concern in the subsonic speed range., however, in the supersonic speed range panels may develop oscillations which cause instability of the structure. This effect has been exhibited experimentally under controlled laboratory conditions motion is limited and buckling may not be a serious design problem. In these cases panel flutter is still of importance because of its effect on the fatigue life and the allowable stresses for design of the panel material. The oscillations of panels may be due either to aerodynamic force induced by the motion of the panel, or to aerodynamic noise, or buffeting (irregular motion induced by turbulence in the flow). The interaction between aerodynamic forces and panel motions, usually referred to as /panel flutter, / has been investigated by several workers in recent years. Since the problem is too complex to be dealt with in its entirety, simplifying assumptions have been made in these investigations. The literature is marked by a certain degree of controversy over the validity of these assumptions and the applicability of the results obtained. A brief review of the literature with reference to several of the approximations made and the results obtained follows.","title":"Review of panel flutter and effects of aerodynamic noise part I.. Panel flutter.","url":"cran.html#doc658"},
{"title":"The gyroscopic effect of a rigid rotating propeller on engine and wing vibration modes.","url":"cran.html#doc42","description":"Scanlan, R.H. And Truman, J.C. J. Ae. Scs. 17, 1950, 653. In many wing vibration analyses it is found necessary to take into account the effect of flexibly mounted engines. Hence, it is reasonable to ask what vibratory gyroscopic effect this flexibility may give rise to when propellers are whirling. An engine mount may be thought of as a horizontal beam cantilevered from the wing, having both horizontal and vertical flexibility. If this beam were infinitely rigid horizontally, then, when it vibrated, the gyroscopic moments induced in the propeller due to the resultant pitching motion of its axis would not produce propeller axis yaw. However, engine-mount lateral stiffness tical stiffness, so that gyroscopic effects will play a role as the propeller axis undergoes pitching vibrations at the tip of the cantilever engine mount. The purpose of this paper is to investigate this role under the assumption that the propeller itself is a rigid disc. The paper is divided into four parts. Part (1) deals briefly with classical gyroscope theory. Part (2) presents engine vibration mode studies-experimental photographic techniques on a model gyroscope mounted at the ends of two different cantilever beams. Part (3) presents the theory of the coupled motion of an elastic wing upon which a gyroscope is mounted to simulate an engine-propeller system on an airplane. Part (4) consists of an example of the theory of part (3), in which, by taking what are thought to be reasonable parameters, results are obtained showing how the whirling of a rigid propeller may materially affect wing normal mode shapes and frequencies."},
{"title":"On a particular class of similar solutions of the equations of motion and energy of a viscous fluid.","url":"cran.html#doc300","description":"Reeves, B.L. And Kippenhan, C.J. J. Ae. Scs. 29, 1962. By introducing the similarity concept to the two-dimensional, incompressible navier-stokes equations and energy equation, a particular class of solutions is found. Two general types of flows are considered.. (1) laminar free convection--I.E., flows which take place due to a body force--and (2) laminar forced convection. For free convection on vertical plates, similar solutions are obtained for two different power-law surface temperature variations, and it is shown that one of these solutions constitutes a new type of boundary problem. Results of numerical integrations of the equations are compared with solutions of the similar boundary-layer equations for free convection, and it is demonstrated that a range of surface temperature variations exists for which the boundary layer equations are no longer valid. For forced convection, it is shown that the use of similarity transformations provides an alternate method of deriving the ordinary differential equations for some well-known solutions, such as couette and stagnation point flows. Solutions are obtained for radial converging or diverging flows between plane surfaces when the temperatures of the surfaces vary as arbitrary powers of the distance from the orgin. Results of numerical integrations of the ordinary differential equations are presented for prandtl numbers of 0.01 and 1.0 and for linear surface temperature variations. Some rather surprising results are obtained for diverging flows when separation occurs and some revealing comparisons with results from boundary-layer theory are made."},
{"description":"Gravitz, S.I., laidlaw, W.R., bryce, W.W. And Cooper, R.E. J.ae.scs. 29, 1962, 445. The quasi-steady approach to flutter utilizes experimental or theoretical steady-state aerodynamic data to arrive at increased understanding of the flutter mechanism, and also, in many cases, acceptably accurate quantitative flutter predictions. Circulation lag effects are neglected, but aerodynamic damping is included in the evaluation of the air forces. Situations requiring the inclusion of rate aerodynamics for accurate flutter estimation are specified. A quasi-unsteady approach is also discussed, in which the approximate magnitude of the circulation lag function at flutter is included in simple modifications of quasi-steady parameters. Closed-form solutions are derived for the flutter characteristics of a typical section with and without rate aerodynamics. Application is then made to the rational flutter analysis of three-dimensional multi-degree-of-freedom lifting surfaces. A specific planform is evaluated in the mach-number range from zero to two. Quasi-steady, quasi-unsteady, and kernel-function results are compared subsonically. Quasi-steady results are utilized supersonically. Primary applications of the quasi-steady approach are in the areas of preliminary design and parameter-variation studies, modification of more sophisticated flutter theories to force compatibility with available steady-state data, and flutter evaluation of complex configurations which can be rationally analyzed by steady-state aerodynamic theories, but for which no complete unsteady aerodynamic theories are presently available.","title":"Development of a quasi-steady approach to flutter and correlation with kernel-function results.","url":"cran.html#doc753"},
{"description":"Vaglio-laurin, R. And Trella, M. Pibal R.623, 1960. Complete inviscid flow fields about three model axisymmetric configurations have been determined numerically. Configurations decreasing bluntness) and flight conditions have been selected so as to indicate separately effects of nose shape, drag coefficient, flight mach number, and thermodynamic behavior of the gas (either ideal calorically perfect gas or air in equilibrium dissociation). Results are presented for thirteen cases. Particular attention is devoted to interpretation and, when possible, correlation of pressure distributions on, and shock shapes about, the cylindrical afterbodies. It is found that.. (a) the correlation of pressure distributions on bodies having nonspherical noses involves interpretive modifications of the law suggested by blast wave analogy. Also shocks about these bodies are not described by parabolae,. (b) for all configurations there is substantial influence of gas behavior on shock shape,. This, however, can be correlated in terms of the gas conditions along a generally defined streamline,. (c) the shock layer can generally be divided into two regions (the first bound by the body and the aforementioned streamline, the second delimited by this streamline and the shock) wherein flow properties can either be approximated by simple laws or correlated.. (d) for each configuration knowledge of the complete flow field in one flight condition (even pertaining to ideal gas flow) can be used to estimate features of flows under general flight conditions including those where equilibrium dissociation is encountered.","title":"A study of flow fields about some typical blunt-nosed slender bodies.","url":"cran.html#doc456"},
{"title":"Thermal diffusion effects on energy transfer in a turbulent boundary layer with helium injection.","url":"cran.html#doc646","description":"Tewfik, O.E., eckert, E.R.G. And Shirtliffe, C.J. To be presented at the 1962 heat transfer and fluid mech.inst. Seattle, A circular cylinder with two-inch diameter and with a porous wall fabricated out of woven wire material was aligned with its axis parallel to an air stream with approximately 100 ft sec velocity. Helium gas was injected into the turbulent boundary layer through the cylinder walls at a uniform rate in the range 1.55 x 10 to 1.08 x 10 of the free stream mass velocity. The local energy transfer along the cylinder was measured at various values of the wall temperature level for the situation that the energy flows from the cylinder to the boundary layer and vice versa. The results showed clearly that the wall temperature for zero energy transfer - the adiabatic wall temperature - was larger than the free stream temperature by up to about 40 f, although viscous dissipation effects are negligible. This temperature excess increases with increasing injection rate and is independent of reynolds number. An analysis in which the laminar sublayer is treated as couette flow with helium injection and which includes thermal diffusion in this layer is formulated. The results show appreciable thermal diffusion effects on adiabatic wall temperature, increasing it over its value for zero injection by amounts of the same order of magnitude as found by measurements. Thermal diffusion however has negligible effects on the heat transfer coefficient. Its effects on the concentration and temperature distribution are discussed and are shown to produce appreciable modifications in the latter."},
{"url":"cran.html#doc179","title":"An analysis of base pressure at supersonic speeds and comparison with experiment.","description":"Chapman, D. Naca tn.2137, 1950. In the first part of the investigation an analysis is made of base pressure in an inviscid fluid, both for two-dimensional and axially-symmetric flow. It is shown that for two-dimensional flow, and also for the flow over a body of revolution with a cylindrical sting attached to the base, there are an infinite number of possible solutions satisfying all necessary boundary conditions at any given free-stream mach number. For the particular case of a body having no sting attached only one solution is possible in an inviscid flow, but it corresponds to zero base drag. Accordingly, it is concluded that a strictly inviscid-fluid theory cannot be satisfactory for practical applications. Since the exact inviscid-fluid theory does not adequately describe the conditions of a real fluid flow, an approximate semi-empirical theory for base pressure in a viscous fluid is developed in a second part of the investigation. The semi-empirical theory is based partly on inviscid-flow calculations, and is restricted to airfoils and bodies without boat-tailing. In this theory an attempt is made to allow for the effects of mach number, reynolds number, profile shape, and type of boundary-layer flow. The results of some recent experimental measurements of base pressure in two-dimensional and axially-symmetric flow are presented for purposes of comparison. Some experimental results also are presented concerning the support interference effect of a cylindrical sting, and the interference effect of a reflected bow wave on measurements of base pressure in a supersonic wind tunnel."},
{"description":"Sacks, A.H. Naca tn.3283, 1954. The problem of determining the total forces, moments, and stability derivatives for a slender body performing slow maneuvers in a compressible fluid is treated within the assumptions of slender-body theory. General expressions for the total forces (except drag) and moments are developed in terms of the geometry and motions of the airplane, and formulas for the stability derivatives are derived in terms of the mapping functions of the cross sections. All components of the motion are treated simultaneously and second derivatives as well as first are obtained, with respect to both the motion components and their time rates of change. Coupling of the longitudinal and lateral motions is thus automatically included. A number of general relationships among the various stability derivatives are found which are independent of the configuration, so that, at most, only 35 of a total of 325 first and second derivatives need be calculated directly. Calculations of stability derivatives are carried out for two triangular wings with camber and thickness, one with a blunt trailing edge, and for two wing-body combinations, one having a plane wing and vertical fin. The influence on the stability derivatives of the squared terms in the pressure relation is demonstrated, and the apparent mass concept as applied to slender-body theory is discussed at some length in the light of the present analysis. It is shown that the stability derivatives can be calculated by apparent mass although the general expressions for the total forces and moments involve additional terms.","url":"cran.html#doc599","title":"Aerodynamic forces, moments and stability derivatives for slender bodies of general cross section."},
{"description":"Falangan, R.A. And Janos, J. J. Nasa tn d-893, 1961. 0. An investigation at a reynolds number per foot of 14.4 x 10 was made to determine the pressure loads produced on a flat-plate wing by rocket jets exhausting in a spanwise direction beneath the wing and perpendicular to a free-stream flow of mach number 2.0. The ranges of the variables involved were /1/ nozzle types - one sonic /jet mach number of two-dimensional supersonic /jet mach number of 1.71/,. /2/ vertical nozzle positions beneath the wing of 4, 8, and 12 nozzle-throat diameters,. And /3/ ratios of rocket-chamber total pressure to free-stream static pressure from 0 to 130. The incremental normal force due to jet interference on the wing varied from one to two times the rocket thrust and generally decreased as the pressure ratio increased. The chordwise coordinate of the incremental-normal-force center of pressure remained upstream of the nozzle center line for the nozzle positions and pressure ratios of the investigation. The chordwise coordinate approached zero as the jet vertical distance beneath the wing increased. In the spanwise direction there was little change due to varying rocket-jet position and pressure ratio. Some boundary-layer flow separation on the wing was observed for the rocket jets close to the wing and at the higher pressure ratios. The magnitude of the chordwise and spanwise pressure distributions due to jet interference was greatest for rocket jets close to the wing and decreased as the jet was displaced farther from the wing. The design procedure for the rockets used is given in the appendix.","title":"Pressure loads produced on a flat-plate wing by rocket jets exhausting in a spanwise direction below the wing and perpendicular to a free-stream flow of mach number 2.0.","url":"cran.html#doc696"},
{"description":"Newman, M. And Forray, M. Proc. Aerospace forum i session, S.M.F. Paper ff-30, 1962, 56. This paper is concerned with the nonlinear axisymmetric analysis of circular plates with in-plane edge restraint. Both temperature and mechanical loads are accommodated as an extension of investigations performed for the isothermal mechanical loading problem. An exact mathematical formulation within the framework of the V. Karman large strain-displacement relations is developed. The equilibrium equations and boundary conditions are then derived by utilizing the calculus of variations for arbitrary axisymmetrical temperatures and normal distributed loading. The satisfaction of equilibrium and compatibility equations requires the solution of two simultaneous nonlinear ordinary differential equations subject to the prescribed boundary conditions. Analytical solutions of such equations are apparently not possible and therefore numerical procedures must be employed. A finite difference procedure utilizing /relaxed iterations, / developed by H. Keller and E. Reiss, and employed by them for the solution of isothermal problems with apparently unlimited load parameter ranges, is used here for combined thermo-mechanical problems. Numerical results are presented for the special case of a simply supported circular plate with radially immovable boundaries, subject to a uniform pressure and an arbitrary temperature variation through the thickness tained for a large range of temperature and load parameters. However, because of space limitations, only a limited amount of data are presented in this paper.","title":"Axisymmetric large deflections of circular plates subjected to thermal and mechanical load.","url":"cran.html#doc1056"},
{"url":"cran.html#doc966","title":"On fully developed channel flows,. Some solutions and limitations, and effects of compressibility, variable properties, and body forces.","description":"Maslen, S.H. Nasa tr r-34, 1959 Some solutions and limitations, and effects of compressibility, variable properties, and body forces. An examination of the effects of compressibility, variable properties, and body forces on fully developed laminar flows has indicated several limitations on such streams. In the absence of a pressure gradient, but presence of a body force liquid this follows also for the case of a constant streamwise pressure gradient. These motions are exact in the sense of a couette flow. In the liquid case two solutions /not a new result/ can occur for the same boundary conditions. An approximate analytic solution was found which agrees closely with machine calculations. In the case of approximately exact flows, it turns out that for large temperature variations across the channel the effects of convection /due to, say, a wall temperature gradient/ and frictional heating must be negligible. In such a case the energy and momentum equations are separated, and the solutions are readily obtained. If the temperature variations are small, then both convection effects and frictional heating can consistently be considered. This case becomes the constant-property incompressible case /or quasi-incompressible case for free-convection flows/ considered by many authors. Finally, there is a brief discussion of cases wherein streamwise variations of all quantities are allowed but only in such form that the independent variables are separable. For the case where the streamwise velocity varies inversely as the square root of distance along the channel, a solution is given."},
{"description":"Dosanjh, D.S. And Sheerlan, W.J. Aiaa jnl. 1963, 1, 329. Experiments on the interaction of transversely impinging two-dimensional jet flows were performed in which a low pressure control jet flow interacted with a relatively high pressure power jet flow. The ratio of the control jet to the power jet supply chamber gauge stagnation pressure was adjusted at 0, 10, and 15. Shadowgraphs of the power jet alone, as well as the corresponding interacting jet flows, were recorded to establish the nature of and changes in the shock structure. The jet flows were traversed by a pitot tube to record the pitot pressure distributions at various locations downstream of the power jet exit. It was discovered that with the addition of only a small percent control jet flow, the normal shock front of the highly underexpanded power jet flow changed to an oblique shock structure and, downstream of the previous location of the normal shock which appeared in the power jet flow alone, the maximum recovery stagnation pressures were proportionally much higher. The mechanism for this behavior of the normal shock is proposed. Possible practical importance of this behavior of interacting jet flows with reference to aerodynamic noise, supersonic diffuser losses, etc., is also pointed out. For the power jet flow alone it was found that by considering the actual jet boundaries as simply an extension of the actual nozzle, the average axial flow quantities, computed from the area-mach number relation using the observed cross-sectional area of the jet flow, agreed quite favorably with the experimental results.","title":"Experiments with two-dimensional, transversely impinging jets.","url":"cran.html#doc1195"},
{"description":"Walker, H.J. And Maillard, W.C. Naca rm a55c08, 1955. An investigation has been made of the possibility of correlating airfoil section data with measured pressure distributions over a 45 sweptback wing in the mach number range from 0.50 to 0.95 at a free-stream reynolds number of approximately 2 million. The wing had an aspect ratio of 5.5, a taper ratio of 0.53, naca 64a010 sections normal to the quarterchord line, and was mounted on a slender body of revolution. At mach numbers of 0.85 and below, and for wing normal-force coefficients below the maximum normal-force coefficient for an infinite-aspect-ratio wing yawed 45 to the flow (derived from airfoil section data by simple sweep relations), good correlation was obtained over most of the wing between wing-section and two-dimensional-airfoil pressure distributions. For greater normal-force coefficients lateral boundary-layer flow permitted the inboard wing sections to rise to high maximum section normal-force coefficients. The effectiveness of this lateral boundary-layer flow disappeared towards the tip. For all mach numbers, the influence of plan-form effects on the pressure distributions limited the quality of the correlation at the 20- and 95-percent-semispan stations. Above a mach number of about 0.85 the shock waves originating at the juncture of the body and the wing trailing edge spread over the span, preventing further application of two-dimensional data. The spanwise load distributions at moderate normal-force coefficients could be predicted from span-loading theory for the entire mach number range of the tests.","url":"cran.html#doc205","title":"A correlation of airfoil section data with the aerodynamic loads measured on a 45 sweptback wing at subsonic mach numbers."},
{"description":"Faulders, C.R. J. Ae. Scs. 1962, 76. The reduction of heat transfer in the laminar boundary layer under the condition of vaporizing ablation is analyzed for arbitrary molecular weight of the vapor. Primary assumptions are that the pressure gradient is zero, the individual components of the binary system are perfect gases, the prandtl number is constant, and the viscosity is proportional to temperature. Variations through the boundary layer of the schmidt number for binary diffusion and the density-viscosity product, are included in the analysis. The wall temperature is held constant. Numerical results are obtained for prandtl numbers of 0.75 and varying from 0.25 to 4.00, wall concentration of the foreign gas as high as 0.9 (corresponding to the high heat rates encountered during re-entry), and ratio of specific heats of foreign gas equal to that of air. Kinetic theory is used to obtain schmidt number as a function of molecular weight and concentration. The departure of schmidt number and prandtl number from unity and the variation of reynolds analogy factor with prandtl number, blowing parameter, wall concentration, and molecular weight ratio are found to have relatively minor influence on the heat block ratio at high rates of ablation. The primary factor governing the influence of molecular weight ratio on the heat block ratio is the variation of across the boundary layer. Little loss of accuracy is incurred, in the range of molecular weight ratios considered here, by assuming schmidt and prandtl numbers of unity as long as the variation is properly taken into account.","title":"Heat transfer in the laminar boundary layer with ablation of vapor of arbitrary molecular weight.","url":"cran.html#doc1226"},
{"url":"cran.html#doc1097","title":"Experimental ablation cooling.","description":"Bond, A.C., rashis, B. And Levin, L. Naca rm.l58e15a, 1958. This paper presents the results of an experimental investigation on the ablation of a number of promising materials for heating conditions comparable to those which may be encountered by unmanned reentry satellite vehicles, as well as for higher heating conditions comparable to those associated with reentry ballistic missiles. Materials tested included the plastics teflon, nylon, and lucite,. The inorganic salts ammonium chloride and sodium carbonate,. Graphite,. A phenolic resin and fiber glass composition,. And The commercial material haveg rocketon. Results of these tests indicated heat-absorption capabilities which are several times greater than those of current metallic heat-sink materials. The results with teflon showed that for hemispherical noses there was no apparent effect of size or stagnation-point pressure on ablation rate for the range of variables covered in the tests. For flat-faced configurations, however, there was a definite increase in the ablation rate with increased stagnation-point pressure. The results for the several materials tested at heating rates associated with reentry ballistic missiles showed considerable increase in the effective heats of ablation over the results obtained at lower heating rates. This trend of increased effectiveness with increased heating potential is in agreement with the predictions of ablation theories. Comparisons of the results for several materials tested at the higher heating rates showed graphite to have the lowest ablation rate of all materials tested."},
{"url":"cran.html#doc1218","title":"Experimental lift and drag of a series of glide configurations at mach numbers 12.6 and 17.5.","description":"Geiger, R.E. J. Ae. Scs. 1962, 410. 6 and 17.5. A series of semiballistic-type bodies consisting of three half sphere cones of 0.3 bluntness ratio with half-cone angles of 8.6, laboratory hypersonic shock tunnel at m = 17.5 and 12.4. In addition, a representative winged glide configuration consisting of a sharp-edged, 60 swept delta wing with cone-segment the range of angle of attack for the half sphere-cone tests was the technique for force coefficient determination consists of analyzing high-speed motion pictures of the motion of very light balsa and isofoam plastic models which are literally free-flown for several milliseconds in the test section of the shock tunnel. Because of viscous effects the newtonian prediction of half sphere cone drag is consistently less than, but generally parallel these bodies is generally well predicted by the newtonian theory except at small and moderate positive angles of attack where it is generally less than newtonian. This lift deficiency appears to increase with cone half angle. Maximum lift-drag ratios fall considerably short of the newtonian predictions. Several exploratory tests at mach 11.7 and low reynolds number ( approximately reduction in) on the 13 model produced an approximate doubling of minimum drag and a 35 percent decrease in (l d) max,. This demonstrates the importance of viscous effects for blunt bodies in the reynolds number range of these tests. The sharp leading-edge, 60 sweep delta wing-body configuration exhibited the same (l d) max, as the wing alone, about 2.80 at both positive and negative angles of attack."},
{"url":"cran.html#doc1137","title":"On the theory of thin elastic toroidal shells.","description":"Clark, R.A. J. Math. Phys. 29, 1950, 146. The author obtains asymptotic solutions to the problem of rotationally symmetric small deflection of thin toroidal elastic shells. He first reduces the problem to that of integrating a single linear nonhomogeneous ordinary differential equation involving two parameters. Asymptotic formulae for the complementary function are obtained by applying the general method of langer (trans.amer.math.soc.33, advantage of yielding results valid near the points where the tangent plane is perpendicular to the axis of revolution, where the methods of asymptotic integration customary in shell theory fail (see the preceding review). For two problems in which only the complementary function is required, the author's results are compared with those obtained by wissler (dissertation, zurich, 1916) by a method of power series expansion,. The agreement is within 4 or better. The author observes that the usual method of obtaining asymptotic expressions for a particular integral, being based on using as an approximation the complementary function obtained from the membrane theory, will fail near points where the tangent plane is perpendicular to the axis of revolution. He therefore introduces a new method, which he states was developed jointly with E. Reissner. He applies his results to the cases of an joint loaded symmetrically and parallel to its axis, a corrugated pipe subject to axial load, and a corrugated cylinder subject to axial pressure. Many numerical calculations are involved and there are two tables of functions occuring in the solutions."},
{"title":"Real gas effects in flow over blunt bodies at hypersonic speeds.","url":"cran.html#doc1319","description":"Nagamatsu, H.T., geiger R.E. And Sheet, R.E. Arc 21, 083, june 1959. A hypersonic shock tunnel has been developed to investigate the aerodynamic characteristics of flow over bodies at conditions comparable to those encountered by ballistic missiles and satellites re-entering the atmosphere. Some results for a shock velocity of over 50, 000 ft/sec in the shock tube portion of the facility are presented. Static pressure investigations were made in the nozzle for different stagnation conditions in order to determine the flow condition and the expansion process. The results of the investigation on representative blunt bodies at hypersonic mach numbers and nozzle stagnation temperatures up to approximately 6000degreek are presented. These include body pressure distributions, shock wave shapes, detachment distances, and photographs of the luminous gas region in the shock layer. It is seen that the shock detachment distance is smaller at higher stagnation temperatures owing to the real gas effects. For the hemisphere the pressure distribution was less than that predicted by the modified newtonian theory for all stagnation temperatures. For a 50degree cone-hemisphere the pressure distribution and the shock wave detachment distance were appreciably affected by the real gas effects. The experimentally obtained shock wave shape and the approximate boundary layer on a flat plate are correlated with the analytical prediction. Some preliminary results for the detached shock wave produced by a blunt two-dimensional body in a low density flow at a mach number of 19.6 are presented."},
{"url":"cran.html#doc1108","title":"A study of second-order supersonic flow theory.","description":"Vandyke, M.D. Naca R.1071, 1952. An attempt is made to develop a second approximation to the solution of problems of supersonic flow which can be solved by existing first-order theory. The method of attack adopted is an iteration process using the linearized solution as the first step. For plane flow it is found that a particular integral of the iteration equation can be written down at once in terms of the first-order solution. The second-order problem is thereby reduced to an equivalent first-order problem and can be readily solved. At the surface of an isolated body, the solution reduces to the well-known result of busemann. The plane case is considered in some detail insofar as it gives insight into the nature of the iteration process. Again, for axially symmetric flow the problem is reduced to a first-order problem by the discovery of a particular integral. For smooth bodies, the second-order solution can then be calculated by the method of von karman and moore. Bodies with corners are also treated by a slight modification of the method. The second-order solution for cones represents a considerable improvement over the linearized result. Second-order theory also agrees well with several solutions for other bodies of revolution calculated by the numerical method of characteristics. For full three-dimensional flow, only a partial particular integral has been found. As an example of a more general problem, the solution is derived for an inclined cone. The possibility of treating other inclined bodies of revolution and three-dimensional wings is discussed briefly."},
{"description":"A method for estimating allowable load capacities of columns subject to creep is presented. The method, which utilizes approximate stress distributions derived from isochronous-stress-strain curves to estimate column load capacities, is shown to be conservative for the time for which the estimate is made. An application of the method is made to test data on as-received and on stabilized 24s-t4 aluminum alloy. A comparison of the computed column capacities with experimental capacities indicates that the method is satisfactory for estimating the decrease in capacity with increasing time. Easily obtained, time-dependent tangent-modulus loads are discussed. They are interpreted as being approximations to allowable load-capacity estimates. A limited application is made to test data, and the results appear promising. It is concluded that if certain limitations are recognized, the method may prove to be useful because of its simplicity. A presentation of the results of an experimental investigation of the effects of column imperfection and column-material variation is made. It is found that column-capacity variations of the order of 10 per cent can result from column-imperfection differences and column-material variation. The results of an experimental study of the variation of column capacity with temperature of exposure are presented. They indicate that column efficiency, as measured by decrease in capacity, can be acceptable for very short times at the higher temperatures. The efficiency at these higher temperatures falls rapidly, however, with increasing time.","title":"Note on creep buckling of columns.","url":"cran.html#doc1019"},
{"description":"Mazelsky, B. Naca tn 2562, 1951. 7. The reciprocal equations for relating the incompressible circulatory indicial lift to the lift due to harmonic oscillations have been modified to include the noncirculatory lift associated with apparent-mass effects. Although the apparent-mass effects are impulsive in nature in incompressible flow, the lift due to apparent-mass effects in compressible flow is a time-dependent function. The corresponding reciprocal equations for the total compressible lift are given. By use of the reciprocal equations for compressible flow, the indicial lift and moment functions due to an airfoil's experiencing a sudden acquisition of vertical velocity are determined numerically for mach number 0.7. Lack of sufficient flutter coefficients prevents the calculation of these functions at other mach numbers. Although the indicial lift and moment functions due to penetration of a sharp-edge gust may be obtained from the oscillatory tab or aileron coefficients by a similar analysis, sufficient coefficients are not available at the present. However, an approximate method is shown for determining a portion of this unsteady-lift function. When a comparison is made of the indicial lift functions at mach numbers appears to be less rapid for the compressible case than for the incompressible case. Consequently, the calculation of the gust load factor at high subsonic mach numbers utilizing the two-dimensional incompressible indicial lift functions and an over-all correction for compressibility such as the prandtl-glauert factor might be conservative.","url":"cran.html#doc701","title":"Numerical determination of indical lift of a two-dimensional sinking airfoil at subsonic mach numbers from oscillatory lift coefficients with calculations for mach number 0.7."},
{"title":"Hypersonic shock layer theory of the stagnation region at low reynolds number.","url":"cran.html#doc667","description":"Cheng, H.K. Proc. 1961, heat transfer and fluid mech. Inst. Stanford. Univ. Press. 1961. P.161 Cheng, H.K. Hypersonic flow at low reynolds number is studied utilizing the shock-layer concept. The present formulation takes into account the salient features of the transport processes within the shock layer in a manner consistent with the shock-layer approximation. The rankine-hugoniot shock relations are modified to include contributions due to heat conduction and viscous effects immediately behind the shock. The specific problem of an axisymmetric stagnation region is treated. The flow regimes for this problem can be classified according to whether or not the transport effects are important immediately behind the shock. In one regime where the ordinary rankine-hugoniot relations hold across the shock, the vorticity-interaction theory based on the boundary-layer approximation is shown to be sufficient. In the other regime where the rankine-hugoniot relations have to be modified but the continuum-flow model applies, an approximate, an analytical solution is obtained. This solution reveals a substantial reduction of the temperature behind the shock and of the shock stand-off distance in the presence of strong surface cooling. The present study is intended to provide a knowledge to bridge the gap between the free-molecule flow regime and that of the boundary layer via the continuum theory. In this respect, the solution obtained appears to be satisfactory in that it yields the correct free-molecule limits for the skin friction and surface-heat transfer rate."},
{"description":"Vaglio-laurin, R. J. Ae. Scs. 1962, 185. Detailed analysis of the subsonic and transonic portious of the flow field about either very blunt or asymmetric configurations requires successive approximations,. These can be carried out in a systematic fashion only when an appropriate convergent perturbation procedure is available. The problem of producing successively refined sets of initial conditions for either /direct/ or /inverse/ analysis of the flow is formulated in the following terms.. Given reasonable estimates for shock shape and pressure distribution on the body, can one determine the flow field of interest to any desired degree of approximation by a perturbation approach.qm a procedure to this effect is developed which involves stretching of coordinates in the spirit of the poincare-lighthill-kuo are transformed along body, shock, and intermediate lines so as to annul perturbations of the local resultant velocity,. (b) for the integral method the coordinate along the boundary of each strip is shifted so as to control perturbations of the velocity component that determines the critical point. The approach is justified by a study of the equations governing the direct method, and by consideration of model transonic flow problems for which closed form solutions are available. The range of validity of the proposed procedure is assessed by practical application and comparison with experiment,. Results are presented for a disk set normal to a low-termperature air stream at m = 4.76, and for a highly asymmetric two-dimensional configuration at m = 8.","title":"On the plk method and the supersonic blunt-body problem.","url":"cran.html#doc1224"},
{"description":"Howarth, L. Proc.roy.S.a, 164, 1938, 547. The problem of the flow along a flat plate placed edgewise to a steady stream, when a retarding pressure gradient varying linearly as the distance x from the leading edge of the plate is superposed is discussed. If y denotes distance measured perpendicular to the plate, a solution is obtained in the form of a power series in x where coefficients are functions of. Differential equations are obtained for these coefficients. Seven of the coefficients have been obtained with reasonable accuracy, and the eighth and ninth roughly. Unfortunately it appears that about eight more terms are required to carry the solution to the point of separation,. The work involved in their determination is prohibitive. Two approximate methods have been developed for determining the error when the first seven terms of the series are used as an approximation. These methods lead to the determination of the point of separation and are in agreement as to its position. If is the velocity at the edge of the boundary layer at the leading edge of the plate and is the velocity gradient, separation is found when. A method is developed for the solution of the boundary layer equations in any retarded region. It is obtained by replacing the velocity distribution at the edge of the boundary layer by a circumscribing polygon of infinitesimal sides and applying the preceding solution to each of these sides, making the momentum integral continuous at each vortex. The problem is thereby reduced to the solution of a first order differential equation.","title":"On the solution of the laminar boundary layer equations.","url":"cran.html#doc155"},
{"description":"Dixon, S.C. Nasa tn.d1485, 1962. 0 of effects of thermal stress and buckling on flutter characteristics of flat single-bay panels of length-width ratio 0. 96. Flat, single-bay, skin stiffener panels with length-width ratios of 0.96 were tested at a mach number of 3.0, at dynamic pressures ranging from 1, 500 to stagnation temperatures from 300 f to effects of thermal stress and buckling on the flutter of such panels. The panel supporting structure allowed partial thermal expansion of the skins in both the longitudinal and lateral directions. Panel skin material and skin thickness were varied. A boundary faired through the experimental flutter points consisted of a flat-panel portion, a buckled-panel portion, and a transition point, at the intersection of the two boundaries, where a panel is most susceptible to flutter. The flutter region consisted of two fairly distinct sections, a large-amplitude flutter region and a small-amplitude flutter region. The results show that an increase in panel skin temperature flutter. The flutter trend for buckled panels is reversed. Use of a modified temperature parameter, which approximately accounts for the effects of differential pressure and variations in panel skin material and skin thickness, reduced the scatter in the data which resulted when these effects were neglected. The results are compared with an exact theory for clamped panels for the condition of zero midplane stress. In addition, a two-mode /transtability/ solution for clamped panels is compared with the experimentally determined transition point.","title":"Experimental investigation at mach number of 3. 0 of effects of thermal stress and buckling on flutter characteristics of flat single-bay panels of length-width ratio 0. 96.","url":"cran.html#doc766"},
{"url":"cran.html#doc486","title":"Similarity laws for aerothermoelastic testing.","description":"Dugundji, J. J.ae.scs. 29, 1962, 935. The similarity laws for aerothermoelastic testing are presented in the range. These are obtained by making nondimensional the appropriate governing equations of the individual external aerodynamic flow, heat conduction to the interior, and stress-deflection problems which make up the combined aerothermoelastic problem. For the general aerothermoelastic model, where the model is placed in a high-stagnation-temperature wind tunnel, similitude is shown to be very difficult to achieve for a scale ratio other than unity. The primary conflict occurs between the free-stream mach number reynolds number aeroelastic parameter heat conduction parameter and thermal expansion parameter. Means of dealing with this basic conflict are presented. These include (1) looking at more specialized situations, such as the behavior of wing structures and of thin solid plate lifting surfaces, and panel flutter, where the aerothermoelastic similarity parameters assume less restrictive forms, (2) the use of /incomplete aerothermoelastic/ testing in which the pressure and/or heating rates are estimated in advance and applied artificially to the model, and (3) the use of /restricted purpose/ models investigating separately one or another facet of the complete aerothermoelastic problem. Some numerical examples of modeling for the general aerothermoelastic case as well as for the specialized situations mentioned in (1) above are given. Finally, extension of the aerothermoelastic similarity laws to higher speeds and temperatures is discussed."},
{"description":"Weinstein, A., rock, D.H. Q. App. Math. 2, 1944, 262. The present paper contains an application of a recently developed variational method to the boundary value problem of the bending of a clamped plate of arbitrary shape. It will be shown that this problem can be linked to the simpler problem of the equilibrium of a membrane by a chain of intermediate problems, which can be solved explicitly and in finite form in terms of the membrane problem. In the intermediate problems, the deflection converges uniformly in the domain of the plate of the clamped plate, and the derivatives of all orders of the deflection converge uniformly in every domain completely interior to the plate. (in the ritz method, not even the convergence of the slopes can be guaranteed.) the method yields numerical results for plates of all shapes for which the membrane problem (which we shall call the base problem) admits an explicit solution. As an example we shall consider a clamped square plate under a uniform load. This problem has been the object of numerous investigations, some of which are theoretical, while others are purely numerical, use infinite simple and double series, and operate with an infinite number of linear equations and an infinite number of unknowns. An inspection of the general formulae derived in the present paper, formulae which become simple in numerical applications, would show how some of the numerical methods might be rendered rigorous. The convergence of higher derivatives is of great practical interest for the approximate computation of the stresses.","title":"On the bending of a clamped plate.","url":"cran.html#doc730"},
{"description":"Laurence, J. Naca r1292, 1956. The intensity of turbulence, the longitudinal and lateral correlation coefficients, and the spectra of turbulence in a 3.5 inch-diameter free jet were measured with hot-wire anemometers at exit mach numbers from 0.2 to 0.7 and reynolds numbers from the results of these measurements show the following.. (1) near the nozzle (distances less than 4 or 5 jet diam downstream of the nozzle) the intensity of turbulence, expressed as percent of core velocity, is a maximum at a distance of approximately increasing mach and or reynolds number. At distances greater than 8 jet diameters downstream of the nozzle, however, the maximum intensity moves out and decreases in magnitude until the turbulence-intensity profiles are quite flat and approaching similarity. (2) the lateral and longitudinal scales of turbulence are nearly independent of mach and or reynolds number and in the mixing zone near the jet vary proportionally with distance from the jet nozzle. (3) farther downstream of the jet the longitudinal scale reaches a maximum and then decreases approximately linearly with distance. (4) near the nozzle the lateral scale is much smaller than the longitudinal and does not vary with distance from the centerline, while the longitudinal scale is a maximum at a distance from the centerline of about mum moves out from the centerline. (6) a statistical analysis of the correlograms and spectra yields a /scale/ which, although different in magnitude from the conventional, varies similarly to the ordinary scale and is easier to evaluate.","url":"cran.html#doc218","title":"Intensity, scale and spectra of turbulence in mixing region of free subsonic jet."},
{"description":"Isakson, G. J. Ae. Scs. 24, 1957, 611. The present work is concerned with the determination of transient temperatures and thermal stresses in simple models intended to simulate parts or the whole of an aircraft structure of the built- up variety subjected to aerodynamic heating. The first case considered is that of convective heat transfer into one side of a flat plate, representing a thick skin, and the effect of the resulting temperature distribution in inducing thermal stresses associated with bending restraint at the plate edges. Numerical results are presented for the transient temperature differentials in the plate when the environment temperature first increases linearly with time and then remains constant, the period of linear increase representing the time of acceleration of the aircraft. Corresponding thermal stress information is presented. The second case is that of the wide-flanged i-beam with convective heat transfer into the outer faces of the flanges. Numerical results are presented for transient temperature differentials for a wide range of values of the applicable parameters and for an environment temperature variation as described above. Corresponding thermal stresses in a beam of infinite length are determined. A theoretical analysis of the stress distribution in a beam of finite length is carried out and numerical results obtained for one case. An experimental investigation of temperatures and stresses in such a beam is described, and results are presented which indicate good agreement with corresponding theoretical results.","title":"A simple model study of transient temperature and thermal stress distribution due to aerodynamic heating.","url":"cran.html#doc29"},
{"url":"cran.html#doc1280","title":"Wings with minimum drag due to lift in supersonic flow.","description":"Ginzel, I. And Multhopp, H. J. Ae. Scs. 1960, 13. It has been shown by R. T. Jones that, in order to produce minimum drag, the given lift must be distributed over the wing surface in such a way that the sum of the downwash induced by this distribution and the downwash induced in reversed flow is constant over the wing surface. This combined downwash can be expressed by an integral which contains the load as a function of the spanwise and chordwise coordinate. The problem of finding the appropriate load distribution is thus reduced to the problem of finding the solution of a rather cumbersome integral equation. The severe spanwise singularity of the kernel function is handled most easily, as in corresponding subsonic problems, by an approximate integration over interpolation polynomials. The chordwise load distribution is represented by a limited series development in legendre polynomials. The sigularity of the kernel function along the mach lines through any pivotal point can be avoided by a similar legendre development of the combined induced downwash which is constant. The integral equation is thus converted into a system of linear equations for the unknown coefficients of the legendre functions of the load distribution at a limited number of spanwise stations. Practical calculations are carried out on an electronic computer. The solutions yield the optimum load distribution and the local incidence (twist, camber, etc.) necessary to realize this distribution. For many wing plan forms, considerable gains over a plane wing appear possible."},
{"url":"cran.html#doc1292","title":"Effect of jet pluming on the static stability of cone-cylinder-flare configurations at a mach number of 9. 65.","description":"Hinson, W.F. And Falanga, R.A. Nasa tn.d1352, 1962. 65. The effects of jet pluming on normal force and pitching moment of have been measured at a free-stream mach number of 9.65 with reynolds numbers based on model length of 500, 000 to 600, 000. Geometric variables included nose bluntness, flare half-angle, and nozzle geometry and exit displacement. Two test nozzles with design mach numbers of 3.74 and 4.60 were operated with compressed air to simulate the initial jet-boundary shape of a particular solid-propellant rocket motor operating between altitudes of 165, 000 and 215, 000 feet. The ratio of the jet pressure to free-stream static pressure varied from a jet-off condition to approximately 1, 300 for the nozzle with design mach number of 3.74, and from a jet-off condition to approximately 280 for the nozzle with design mach number of 4.60. The angle-of-attack range was from 0 to approximately 6. The results indicate that as the jet-pressure ratio was increased the size of the jet plume increased, and as a result the model static stability was decreased. Increasing the angle of attack resulted in a reduction in static instability during the jet-on condition. Increasing nose bluntness resulted in a more forward movement of the center of pressure when jet-plume interference was not present and a rearward movement in the center of pressure when jet interference was present. Increasing the nozzle-area expansion ratio and displacing the nozzle exit downstream of the flare base resulted in a more rearward location of the center of pressure."},
{"title":"Review of published data on the effect of roughness on transition from laminar to turbulent flow.","url":"cran.html#doc96","description":"Hugh L. Dryden National advisory committee for aeronautics A review is presented of the published data on the effect of roughness, especially single roughness elements, on transition from laminar to turbulent flow, in which an attempt is made to reanalyze and correlate the available information. The reanalysis shows that the transition reynolds number of a flat plate with zero pressure gradient is a function of the ratio of the height of the roughness element to the displacement thickness of the boundary layer at the element, this functional relation being a better representation of the data than a constant critical reynolds number of the roughness element. Other data show that the effects of roghness are similar in streams of different initial turbulence and that a plot of the ratio of transition reynolds number of the rough plate to that for the smooth plate against the ratio of the height of the roughness element to displacement thickness of the boundary layer at the element gives good correlation of all the data for a given shape when transition occurs downstream from the roughness element. At a certain value of the height-thickness ratio dependent on the stream speed, location of roughness element, and airstream turbulence, the transition position reaches the element and remains there as the height or the stream speed is further increased. The paper also discusses available data on the effect of distributed roughness on transition on a flat plate, as well as some of the published data on roughness effects on transition on air-foils."},
{"description":"Bray, K.N.C. J. Fluid mech. V.6 part 1, 1-32. July, 1959. The flow of an ideal dissociating gas through a nearly conical nozzle is considered. The equations of one-dimensional motion are solved numerically assuming a simple rate equation together with a number of different values for the rate constant. These calculations suggest that deviations from chemical equilibrium will occur in the nozzle if the rate constant lies within a very wide range of values, and that, once such a deviation has begun, the gas will very rapidly 'freeze'. The dissociation fraction will then remain almost constant if the flow is expanded further, or even if it passes through a constant area section. An approximate method of solution, making use of this property of sudden 'freezing' of the flow, has been developed and applied to the problem of estimating the deviations from equilibrium under a wide range of conditions. If all the assumptions made in this paper are accepted, then lack of chemical equilibrium may be expected in the working sections of hypersonic wind tunnels and shock tubes. The shape of an optimum nozzle is derived in order to minimize this departure from equilibrium. It is shown that, while the test section conditions are greatly affected by 'freezing', the flow behind a normal shock wave is only changed slightly. The heat transfer rate and drag of a blunt body are estimated to be reduced by only about 25 per cent even if complete freezing occurs. However, the shock wave shape is shown to be rather more sensitive to departures from equilibrium.","title":"Atomic recombination in a hypersonic wind tunnel nozzle.","url":"cran.html#doc575"},
{"description":"Smith, J.H.B. And Mangler, K.W. R.A.E. Rep. Aero. 2584. Arc 19, 961, september 1957. In an attempt to avoid flow separation at the leading edge of a thin delta wing with subsonic leading edges, an attachment line is prescribed there. This is done by requiring the load, as predicted by attached flow theory, to vanish along the leading edge at the design lift coefficient. For sonic speed, a complete account of this flow is given in terms of slender wing theory and the load distributions corresponding to arbitrary conical camber are calculated. For supersonic speeds load distributions arising in the slender wing theory are considered and the corresponding conical camber distributions are found by linearized theory. The lift-dependent drag for a given lift is then minimized with respect to the coefficients of a linear combination of these load distributions. It is found that the lift-dependent drag factor for these conically cambered wings approaches the value it takes for the attached flow/in which leading edge suction occurs/past the uncambered wing at the same mach number, as more terms are included in the linear combination. However, when the leading edge is almost sonic an appreciable reduction is predicted. The corresponding load distributions and wing shapes are calculated and drawn. The optimum shapes for a fixed number of terms resemble flat plates drooped downwards near their edges, so that the localised leading edge suction is replaced by a distributed force on a forward-facing surface, producing an effect of similar magnitude.","title":"The use of conical camber to produce flow attachment at the leading edge of a delta wing and to minimize the lift-dependent drag at sonic and supersonic speeds.","url":"cran.html#doc683"},
{"url":"cran.html#doc564","title":"Local heat transfer and recovery temperature on a yawed cylinder at a mach number of 4. 15 and high reynolds numbers.","description":"Beckwith, I.E. And Gallagher, J.J. Nasa memo 2-27-59l, 1959. 15 and high reynolds numbers. Local heat transfer, equilibrium temperatures, and wall static pressures have been measured on a circular cylinder at yaw angles of 0, 10, 20, 40, and 60. The reynolds number range of the tests was from 1x10 to 4x10 based on cylinder diameter. Increasing the yaw angle from 0 to 40 increased the stagnation-line heat-transfer coefficients by 100 to 180 percent. A further increase in yaw angle to heat-transfer coefficients. At zero yaw angle the boundary layer over the entire front half of the cylinder was laminar but at yaw angles of 40 and 60 it was evidently completely turbulent, including the stagnation line, as determined by comparison of local heat-transfer coefficients with theoretical predictions. The level of heating rates and the nature of the chordwise distribution of heat transfer indicated that a flow mechanism different from the conventional transitional boundary layer may have existed at the intermediate yaw angles of 10 and 20. At all yaw angles the peak heat-transfer coefficient occurred at the stagnation line and the chordwise distribution of heat-transfer coefficient decreased monotonically from this peak. The average heat-transfer coefficients over the front half of the cylinder are in agreement with previous data for a comparable reynolds number range. The theoretical heat-transfer distributions for both laminar and turbulent boundary layers are calculated directly from simple quadrature formulas derived in the present report."},
{"title":"Theoretical investigations of a supersonic laminar boundary layer with foreign-gas injection.","url":"cran.html#doc1199","description":"Freedman, S.I., radbill, J.R. And Kaye, J. Aiaa jnl. 1, 1963. The phenomena arising from the uniform injection of helium, air, argon, and iodine into the laminar boundary layer of a supersonic stream of air in a tube were investigated theoretically. The partial differential equations describing the energy, mass, and momentum transfers through the boundary layer were obtained, and a series solution was found for the case of uniform injection through the tube wall. The results of the analysis are in the form of axial distributions of wall temperature and recovery factor and of radial distribution of concentration, velocity, static, and stagnation temperatures. The gas mixture was assumed to be a perfect gas. Properties of the mixture were calculated in accordance with the gibbs-dalton rule and the mixing rules based on the kinetic theory of dilute gases. Transport properties for pure air were taken from the N.B.S. Tabulations. Transport properties for the other gases were calculated by kinetic-theory methods, employing a lennard-jones 6-12 model for the interaction potential. The theoretical predictions for the recovery factor along the tube with air or argon injection agree with experimental data to within one percent. The theoretical predictions for helium injection indicate an 8-percent rise in the recovery factor along the tube, while experiments have shown only a 1-percent rise. These differences between theory and experiment are attributed to inaccuracies in the approximations to the transport properties of the binary mixtures."},
{"description":"Bromm, A.F. And O'donnel, R.M. Naca rm l54i16, 1954. An investigation has been conducted in the langley 9-inch supersonic tunnel to determine the jet effects for varying jet mach number and nozzle divergence angle upon the pressure on the base annulus of a model with a cylindrical afterbody. The tests were conducted over a wide range of jet static pressure ratios and at a reynolds number of approximately free-stream mach numbers of 1.62, 1.94, and 2.41. All testing was conducted with an artificially induced turbulent boundary layer along the model. In the lower range of jet static pressure ratios, jet flow from a sonic or supersonic nozzle affected the pressure acting on the base annulus in essentially the same manner as shown in naca rm e53h25 which covers jet static pressure ratios up to about present results showed that the base pressure tends to level off with increasing jet static pressure ratio, and at the extreme static pressure ratios reached in tests with sonic nozzles the base pressure began to decrease. Except in the lower range of jet static pressure ratios, nozzle divergence angle generally had a larger effect on the base pressures than nozzle mach number,. The increase in base pressure for a change in divergence angle from 0 to 10 was small compared to the increase when the divergence angle was changed from and other data indicates that the effects of divergence angle were reduced when the ratio of jet exit diameter to base diameter was decreased. Jet mach number effects increased with increase in stream mach number.","url":"cran.html#doc174","title":"Investigation at supersonic speeds of the effects of jet mach number and divergence angle of the nozzle upon the pressure of the base annulus of a body of revolution."},
{"description":"Biot, M.A. J. Ae. Scs. 24, 1957. New methods are presented for the analysis of transient heat flow in complex structures, leading to drastic simplifications in the calculation and the possibility of including nonlinear and surface effects. These methods are in part a direct application of some general variational principles developed earlier for linear thermodynamics. They are further developed in the particular case of purely thermal problems to include surface and boundary-layer heat transfer, nonlinear systems with temperature-dependent parameters, and radiation. The concepts of thermal potential, dissipation function, and generalized thermal force are introduced, leading to ordinary differential equations of the lagrangian type for the thermal flow field. Because of the particular nature of heat flow phenomena, compared with dynamics, suitable procedures must be developed in order to formulate each problem in the simplest way. This is done by treating a number of examples. The concepts of penetration depth and transit time are introduced and discussed in connection with one-dimensional flow. Application of the general method to the heating of a slab, with temperature-dependent heat capacity, shows a substantial difference between the heating and cooling processes. An example of heat flow analysis of a supersonic wing structure by the present method is also given and requires only extremely simple calculations. The results are found to be in good agreement with those obtained by the classical and much more elaborate procedures.","url":"cran.html#doc395","title":"New methods in heat flow analysis with application to flight structures."},
{"title":"An alternative formulation of the problem of flutter in real fluids.","url":"cran.html#doc363","description":"Chu, W.H. And Abramson, H.N. J. Ae. Scs. 26, 1959. It is well known, in steady flow, that the actual lift curve slope is somewhat less than that predicted by inviscid flow theory, even at small angles of attack. As the stall angle is approached, the lift curve slope continually decreases and thus deviates even more from the theoretical value. Pinkerton employed the measured circulation to determine the pressure distribution and found that the resulting prediction of the moment is considerably improved over that given by the classical theory. This amounts to replacing the conventional kutta-joukowski condition with the condition that the total lift should agree with the measured value, and this, in turn, completely determines the flow pattern. Practically, this is accomplished by giving a fictitious camber to the profile. Since potential flow theory is valid outside of the boundary layer, once the boundary-layer thickness is known, the potential flow may be corrected for the displacement thickness and the viscous wake by appropriate source distributions. The boundary layer cannot be evaluated, of course, until the potential flow is known and the circulation is applied. A criterion to determine the circulation, by generalizing the kutta-joukowski condition, was proposed by preston and spence by assuming that the pressure at the trailing edge shall have the same value when determined from the potential-flow values above and below the airfoil. This procedure gives qualitative information concerning viscous effects in steady flow."},
{"title":"Rapid laminar boundary layer calculations by piece-wise application of similar solutions.","url":"cran.html#doc292","description":"Smith, A.M.O. J. Ae. Scs. 23, 1956. A method is presented for the rapid calculation of the incompressible laminar boundary layer in an arbitrary flow around either a two-dimensional or a rotationally-symmetrical body. The solution is obtained without recourse to von karman's momentum equation by means of a coarse step-by-step procedure in which each segment of the velocity distribution is approximated by one of the falkner-skan family of similar flows. Solutions have at least as much accuracy as those of any other one-parameter approximate method, and in certain cases the solutions become exact. In regions of accelerating velocity, the accuracy appears to be very high. In decelerating flows, separation is predicted somewhat early compared with exact solutions that is, the method is conservative in contrast to the von karman-pohlhausen procedure which sometimes fails to predict separation that actually exists. The method is the most rapid hand procedure known to the author, provided the full history of the boundary layer is required. If only a thickness such as is needed at one point on a surface, then it is about equal in speed to the quadrature method. But, if several values of or other properties along a surface are required, it is appreciably faster than the quadrature method. Characteristically, only four steps are needed between the forward stagnation point and the pressure peak. Once the velocity-distribution data are available, each step in a two-dimensional calculation requires about 5 minutes, using a slide rule."},
{"description":"Havelock, T.H. Proc.roy.S.a, 100, 1922, 499. The general character of experimental results dealing with the effect of shallow water on ship resistance may be stated briefly as follows..--at low velocities the resistance in shallow water is greater than in deep water, the speed at which the excess is first appreciable varying with the type of vessel. As the speed increases, the excess resistance increases up to a maximum at a certain critical velocity, and then diminishes. With still further increase of speed, the resistance in shallow water ultimately becomes, and remains, less than that in deep water at the same speed. The maximum effect is the more pronounced the shallower the water. For further details and references one may refer to standard treatises, but one quotation may be made in regard to the critical velocity.. /this maximum appears to be at about a speed such that a trochoidal wave travelling at this speed in water of the same depth is about times as long as the vessel. It was at one time supposed that the speed for maximum increase in resistance was that of the wave of translation. This, however, holds only for water whose depth is less than for greater depths the speed of the wave of translation rapidly becomes greater than the speed of maximum increase of resistance./ in a recent analysis of the data, H. M. Weitbrecht expresses a similar conclusion by stating that for each depth of water there is a critical velocity, but that the critical velocity does not vary as the square root of the corresponding depth.","url":"cran.html#doc156","title":"The effect of shallow water on wave resistance."},
{"title":"Real gas effects in flow over blunt bodies at hypersonic speeds.","url":"cran.html#doc1274","description":"Nagamatsu, H.T., geiger, R.E. And Sheer, R.E. J. Aero. Sc. April, 1960. P241. A hypersonic shock tunnel has been developed to investigate the aerodynamic characteristics of flow over bodies at conditions comparable to those encountered by ballistic missiles and satellites re-entering the atmosphere. Some results for a shock velocity of over 50, 000 ft. Per sec. In the shock tube portion of the facility are presented. Static pressure investigations were made in the nozzle to determine the flow condition and the expansion process. The results of the investigation of representative blunt bodies at hypersonic mach numbers and nozzle stagnation temperatures up to approximately 6, 000degreek. Are presented. These include body pressure distributions, shock-wave shapes, detachment distances, and photographs of the luminous gas region in the shock layer. It is seen that the shock detachment distance is smaller at higher stagnation temperatures due to the real gas effects. For the hemisphere the pressure distribution was less than that predicted by the modified newtonian theory for all stagnation temperatures. For a 50degree cone-hemisphere the pressure distribution and the shock detachment distance were appreciably affected by the real gas effects. The observed shock-wave shape and the approximate boundary layer on a flat plate are compared with the analytical prediction. Some preliminary results for the detached shock wave produced by a blunt two- dimensional body in a low density flow at a mach number of 19.6 are presented"},
{"title":"Flutter of aerodynamically heated aluminium-alloy and stainless steel panels with length-width ratio of 10 at mach 3. 0.","url":"cran.html#doc859","description":"Guy, L.D. And Bohon, H.L. Nasa tn.d1353, 1962. 0. An investigation of the effects of aerodynamic heating on the flutter of multibay external-skin panels has been carried out at a mach number of 3.0 in the langley 9- by 6-foot thermal structures tunnel. Both aluminum-alloy and 17-7 ph stainless-steel panels with a length-width ratio of 10 for each bay were tested at dynamic pressures between addition, a few tests were made on the lower vertical stabilizer of the x-15 airplane which has external-skin panels unsupported for a length all panels showed flutter boundaries characterized by an increase in panel thickness required to prevent flutter with increasing thermally induced stress prior to buckling. After buckling the panels showed flutter boundaries characterized by a decrease in thickness required to prevent flutter with further increases in thermal stress. The largest thickness required to prevent flutter in the presence of aerodynamic heating occurred at the transition between the flat-panel boundary and the buckled-panel boundary. This peak value (for aluminum-alloy panel) was as much as 60 percent greater than the extrapolated value for an unheated, unloaded panel. Values of the modified-thickness-ratio flutter parameter for the unstressed panels (obtained by extrapolation) were in fair agreement for the aluminum, steel, and x-15 stabilizer panels. Peak values at transition, however, showed large differences due to apparently minor changes in panel-support construction and or changes in panel-skin material."},
{"description":"Arnold, R.N. And Warburton, G.B. J. Proc. I. Mech. E. 167, 1953, 62. The flexural vibrations of the walls of thin cylinders are considered. In this type of vibration many forms of nodal pattern may exist owing to the combination of circumferential and axial nodes. Theoretical expressions are developed for the natural frequencies of cylinders with freely-supported and fixed ends and a comparison is made with the frequencies obtained experimentally. In practice, the ends of cylinders are subjected to a certain degree of fixing by end-plates, flanges, etc., and the natural frequencies thus lie between the corresponding values for freely-supported and fixed ends. To make possible the estimation of such frequencies, a method is devised in which an equivalent wavelength factor is used. This factor represents the wavelength of the freely-supported cylinder that would have the same frequency as the cylinder under consideration when vibrating in the same mode. The results of experimental investigations with various end thicknesses and flange dimensions are recorded, and from these the equivalent factors are derived. Sets of curves calculated for cylinders with freely-supported ends and covering a range of cylinder thicknesses are given. From these it is possible to obtain close approximation to the frequencies of cylinders under other end conditions by the use of an appropriate factor. An example is given of frequency calculations for a large air-receiver for which two frequencies were identified by experiment.","title":"The flexural vibrations of thin cylinders.","url":"cran.html#doc845"},
{"description":"Lina, L.J. And Maglieri, D.J. Nasa tn.d235, 1960. The intensity of shock-wave noise at the ground resulting from flights at mach numbers to 2.0 and altitudes to 60, 000 feet was measured. Measurements near the ground track for flights of a supersonic fighter and one flight of a supersonic bomber are presented. Level cruising flight at an altitude of 60, 000 feet and a mach number of 2.0 produced sonic booms which were considered to be tolerable, and it is reasonable to expect that cruising flight at higher altitudes will produce booms of tolerable intensity for airplanes of the size and weight of the test airplanes. The measured variation of sonic-boom intensity with altitude was in good agreement with the variation calculated by an equation given in nasa technical note d-48. The effect of mach number on the ground overpressure is small between mach numbers of 1.4 and 2.0, a result in agreement with the theory. No amplification of the shock-wave overpressures due to refraction effects was apparent near the cutoff mach number. A method for estimating the effect of flight-path angle on cutoff mach number is shown. Experimental results indicate agreement with the method, since a climb maneuver produced booms of a much decreased intensity as compared with the intensity of those measured in level flight at about the same altitude and mach number. Comparison of sound pressure levels for the fighter and bomber airplanes indicated little effect of either airplane size or weight at an altitude of 40, 000 feet.","title":"Ground measurements of airplane shock wave noise at mach numbers to 2, and at altitudes of 60, 000 feet.","url":"cran.html#doc806"},
{"description":"Clarke, J.F. Coa n102, 1960. The rate of energy transfer between parallel flat plates is evaluated when the (stagnant) gas between them is polyatomic with one inert internal mode. Deviations of the thermal conductivity from the complete equilibrium of the inert mode relaxation time and the effectiveness of the walls in exciting or de-exciting this mode. The results are obtained via a linear theory consistent with small temperature differences between the plates. It is found that the eucken-value of conductivity could be exceeded if the relaxation times are non-zero and the plates very effective in exciting the inert mode. When relaxation times are very short the effect of the walls on the energy transfer rate is small, but the walls make their presence felt by distorting the temperature profiles in /boundary layers/ adjacent to the walls which are of order in thickness time). This result is analogous to hirschfelder's (1956) for the case of chemical reactions. For experimental measurement of conductivity in a hot wire cell type of apparatus it is shown that extrapolation of measured reciprocal conductivities to zero reciprocal pressure should load to the full eucken value. It is also shown that the slope of reciprocal apparent (measured) conductivity versus reciprocal pressure curves is a function of relaxation time as well as of the accommodation coefficients. It is quite possible that the relaxation effect here is comparable with the temperature jump effects, even for rotation in diatomic molecules.","title":"Heat conduction through a gas with one inert internal model.","url":"cran.html#doc168"},
{"title":"Some experimental studies of panel flutter at mach 1.3.","url":"cran.html#doc856","description":"Sylvester, M.A. And Baker, J.E. Naca tn.3914, 1957. 3. Experimental studies of panel flutter were conducted at a mach number of 1.3 to verify the existence of this phenomenon and to study the effects of some structural parameters on the flutter characteristics. Thin rectangular metal plates were used in these studies and were mounted as a section of the tunnel wall. Most of the data were obtained by using aluminum-alloy panels, although a few steel, magnesium, and brass panels were also used. Different materials with various thicknesses and lengths were used to determine the effect of these parameters on panel flutter. The experimental program consisted of three phases.. Panels clamped front and rear, and (3) buckled panels clamped on all four edges. Panel flutter was obtained under controlled laboratory conditions and it was found that, at the flow conditions of these tests, increasing tensile forces were effective in eliminating flutter, as were shortening the panels or increasing the bending stiffness. No apparent systematic trends in the flutter modes or frequencies could be observed, and it is significant that the panel flutter sometimes involved higher modes and frequencies. The presence of a pressure differential between the two surfaces of a panel was observed to have a stabilizing effect. Initially buckled panels were more susceptible to flutter than panels without buckling. Buckled panels with all four edges clamped were much less prone to flutter than buckled panels clamped front and rear."},
{"description":"Wells, W.R. And Armstrong, W.O. Nasa tr r -dash 127, 1962. Closed-form expressions and tables composed from these expressions are presented for complete and partial conic and spheric bodies at combined angles of attack and sideslip in newtonian flow. Aerodynamic coefficients of these bodies are tabulated for various body segments over a range of angles of attack from 1degree to 85degree and angles of sideslip from 0degree to 15degree. Some comparisons between newtonian predictions and hypersonic experimental aerodynamic characteristics were made for conic bodies having various surface slopes, nose bluntnesses, and body cross sections to indicate the range of validity of the theory. In general, the theory is shown to agree quite well with experimental results for sharp-nose complete cones and for configurations having large blunted noses and steep surface slopes. However, agreement between theory and experiment generally is poor for the more slender, slightly blunted complete or half conic bodies and also for sharp-nose half conic bodies where real-flow phenomena such as forebody interference, viscous forces, leeward surface contributions, or leading-edge pressure reductions may have significant effect. The agreement between theory and experiment for the bodies considered can be improved by using the stagnation pressure coefficient behind a normal shock rather than 2 as the newtonian coefficient, although for the sharp-nose half conic bodies there is no theoretical justification for this modification.","url":"cran.html#doc688","title":"Tables of aerodynamic coefficients obtained from developed newtonian expressions for complete and partial conic and spheric bodies at combined angles of attack and sideslip with some comparisons with hypersonic experimental data."},
{"description":"Hauser, C.H., plohr, H.W. And Sonder, G. Naca rm e9k25, 1950. An analysis was made of the flow conditions downstream of a cascade of turbine rotor blades at critical and supercritical pressure ratios. The results of five theoretical methods for determining the deflection angle are compared with those of an experimental method using the conservation-of-momentum principle and static-pressure surveys, and also are compared with an analysis of schlieren photographs of the flow downstream of the blades. A two- dimensional cascade of six blades with an axial width of 1.80 inches was used for the static-pressure surveys and for some of the schlieren photographs. In order to determine the flow conditions several blade chords downstream of the cascade, schlieren photographs were taken of the flow through a cascade of 18 blades having an axial width of 0.60 inch. For the blade design studied, even at static-to-total pressure ratios considerably lower than that required to give critical velocity at the throat section, the flow was deflected in the tangential direction as predicted for the incompressible case. As the pressure ratio was lowered further, the aerodynamic loading of the rear portion of the blade reached a maximum value and remained constant. After this condition was attained, the expansion downstream of the cascade took place with a constant tangential velocity so that no further increase in the amount of turning across the blade row and no further increase in the loading of the blade was available.","url":"cran.html#doc277","title":"Study of flow conditions and deflection angle at exit of two-dimensional cascade of turbine rotor blades at critical and supercritical pressure ratios."},
{"title":"Exact solution of the neumann problem. Calculation for non- circulatory plane and axially symmetric flows about or within arbitrary boundaries.","url":"cran.html#doc266","description":"Smith, A.N.C. And Pierce, J. 3rd nat. Con. App. Mech. 1958. Calculation for non- circulatory plane and axially symmetric flows about or within arbitrary boundaries. An exact general method of solving the neumann or second boundary-value problem has been developed and has been applied to the calculation of low-speed flows about or within bodies of almost any shape, provided the flow is either plane or has axial symmetry. Solid-body, inlet, and purely internal flow problems can be solved. The method is capable of dealing with several bodies at once in the presence of one another, and consequently interference problems can be treated with ease. Boundaries need not be solid, that is, flows involving area suction can be calculated. Velocities can be computed not only for points on the surface of the body but for the entire flow field. A surface source distribution is used as a basis for solution. This leads to a fredholm integral equation of the second kind, which is solved as a set of linear algebraic equations, usually by a modified seidel method. At the present time the solution is programed on the ibm 704 edpm to solve the flow about any body that has the previously mentioned characteristics and whose profile can be defined satisfactorily by no more than 300 coordinate points. A number of solutions are presented, to show both the scope of the method and its accuracy. Computations require from three minutes to two hours, depending upon the shape of the body and the number of points used to define it."},
{"description":"Kendall, J. M. J. Aero. Sc. V. 24, pp 47-56, 1957. 8. The boundary layer on a slender body tends to be very thick at hypersonic speeds. It interacts with the external flow by producing larger flow deflections near the leading edge than those due to the body alone flow around the boundary layer gives rise to an induced pressure with a negative gradient which thins the boundary layer and increases the skin friction with respect to the zero pressure gradient value. Experiments on a flat plate with a sharp leading edge have been performed in the galcit 5-dash by 5-dash in. Mach 5.8 hypersonic wind tunnel. The induced pressure was measured by means of orifices in the plate surface. Profiles of mach number, velocity, mass flow, pressure, and momentum deficiency were calculated from impact pressure surveys normal to the plate surface made at various distances from the leading edge. The results are as follows. /1/ the induced pressures are 25 per cent higher than the weak interaction theory. /2/ the boundary layer and the external flow are distinctly separate for as low as 6, 000. /3/ the shock wave location is in good agreement with that predicted by the friedrichs theory for a body shape equivalent to the observed boundary-layer displacement thickness. /4/ expansion waves reflected from the shock are weak. /5/ the average skin-friction coefficient tends toward and nearly matches the zero pressure gradient value downstream, but increases to approximately twice that value as the leading edge is approached.","title":"An experimental investigation of leading edge shock wave boundary layer interaction at mach 5.8.","url":"cran.html#doc569"},
{"url":"cran.html#doc1370","title":"Some remarks on the flat plate boundary layer.","description":"Lewis, J.A. And Carrier, G.F. Q. App. Math. 7, 1949, 228. The authors discuss the solutions for the flow of a viscous incompressible fluid near the leading edge of a semi-infinite flat plate without pressure gradient. The oseen linearization is employed which approximates the equations of motion and continuity by where are the coordinate directions, the corresponding velocity components and the uniform free stream velocity which is parallel to the plate. Defining a perturbation stream function by the differential equation to be solved is with boundary conditions far from the plate and when y=0 and. The authors discuss the problem by applying the two-dimensional fourier transform and obtain an explicit solution for the velocity gradient at the plate which is in disagreement with the result of the blasius solution. From this the authors conclude that it would be more appropriate to use a velocity other than in the linearization of the equations of motion and suggest replacing by where. This choice does not affect the solution far from the plate but gives on the plate and in comparison with blasius solution indicates that c=0.35. The solution of the modified oseen equation with this value of c then seems acceptable as the approximate solution in the region intermediate between the stokes flow and the free stream. On the basis of these considerations, the authors suggest an iteration procedure for obtaining the exact solution for the above problem as well as a solution for the plate of finite length."},
{"url":"cran.html#doc197","title":"Pressure distributions on three bodies of revolution to determine the effect of reynolds number up to and including the transonic speed range.","description":"Swihart, J.M. And Whitcomb, C.F. Naca rm l53h04, 1953. This paper presents the results of an investigation conducted in the langley 16-foot transonic tunnel to determine the effects of varying reynolds number on the pressure distribution on a transonic body of revolution at angles of attack through the transonic speed range. The effect of a change in sting cone angle on the pressure distributions and a comparison of experimental incremental pressures with theory is also included. The models were tested through a mach number range from 0.60 to 1.09. The reynolds number range based on body length was from 9 x 10 to 39 x diameter was 1.3 x 10 to 4.53 x 10 for the model at 8 angle of attack. An increase in reynolds number from 9 x 10 to 39 x 10 affected the longitudinal pressure distributions very slightly. These effects were of such a nature as to cause an increase of 0.05 in the normal-force coefficient of the body when tested in the subcritical cross-flow reynolds number range. This increase is in agreement with theoretical approximations. A comparison between experimental and theoretical values of the incremental pressure coefficient due to angle of attack indicated good agreement except at angles where separated flow areas existed over the body. The effect of a change in sting-cone angle from 5 to 9 on the pressure distribution of the 120-inch model was negligible up to a mach number of 1.05. At this mach number the effect was to cause a small increase in the velocity over the rear of the body."},
{"description":"Wu, C. Naca tn 2604, 1952. A general theory of steady three-dimensional flow of a nonviscous fluid in subsonic and supersonic turbomachines having arbitrary hub and casing shapes and a finite number of blades is presented. The solution of the three-dimensional direct and inverse problem is obtained by investigating an appropriate combination of flows on relative stream surfaces whose intersections with a z-plane either upstream of or somewhere inside the blade row form a circular arc or a radial line. The equations obtained to describe the fluid flow on these stream surfaces show clearly the several approximations involved in ordinary two-dimensional treatments. They also lead to a solution of the three-dimensional problem in a mathematically two-dimensional manner through iteration. The equation of continuity is combined with the equation of motion in either the tangential or the radial direction through the use of a stream function defined on the surface, and the resulting equation is chosen as the principal equation for such flows. The character of this equation depends on the relative magnitude of the local velocity of sound and a certain combination of velocity components of the fluid. A general method to solve this equation by both hand and high-speed digital machine computations when the equation is elliptic or hyperbolic is described. The theory is applicable to both irrotational and rotational absolute flow at the inlet of the blade row and at both design and off-design operations.","url":"cran.html#doc987","title":"A general theory of three dimensional flow in subsonic and supersonic turbo-machines of axial-radial-and mixed-flow types."},
{"description":"Berndt S.B. Ffa rep. 71, stockholm, 1957. The boundary layers at the test section walls of a transonic wind tunnel are known to reduce the wall interference. In the present paper this effect is studied by means of small perturbation theory, assuming viscosity to be negligible when perturbing a turbulent boundary layer. An approximation for thin boundary layers leads to a modified boundary condition at the wall of the test section, expressing the normal streamline slope induced by changes in mass flow density and crossflow within the boundary layer. This boundary condition is applied to the linearized equations of subsonic flow and to the non-linear transonic equations at choking, the cases of plane and circular test sections only being treated in detail. The results of linear theory show that all corrections except the three-dimensional angle-of-attack correction are considerably reduced by the presence of the boundary layers at mach numbers greater than 0.9, the essential part of their influence being due to the change of mass flow density with pressure. In the case of choking the analysis indicates that the presence of boundary layers will increase the maximum model size for which the flow can be interpreted as corresponding to mach number one in free flight. Finally, the technique of using artificial thickening of the wall boundary layers for a reduction of wall interference is considered, though without reaching a definite conclusion as to its value as compared to other techniques.","url":"cran.html#doc1154","title":"On the influence of wall boundary layers in closed transonic test sections."},
{"url":"cran.html#doc689","title":"Investigation of the laminar aerodynamics heat transfer characteristics of a hemisphere cylinder in the langley 11-inch hypersonic tunnel at a mach number of 6. 8.","description":"Crawford, D.H. And Mccauley, W.D. Naca R.1323, 1957. 8. A program to investigate the aerodynamic heat transfer of a nonisothermal hemisphere-cylinder has been conducted in the langley 11-inch hypersonic tunnel at a mach number of 6.8 and a reynolds number from approximately 0.14x10 to experimental heat-transfer coefficients were slightly less over the whole body than those predicted by the theory of stine and wanlass (naca technical note 3344) for an isothermal surface. For stations within 45 of the stagnation point the heat-transfer coefficients could be correlated by a single relation between local stanton number and local reynolds number. Pitot pressure profiles taken at a mach number of 6.8 on a hemisphere-cylinder have verified that the local mach number or velocity outside the boundary layer required in the theories may be computed from the surface pressures by using isentropic flow relations and conditions immediately behind a normal shock. The experimental pressure distribution at a mach number of velocity gradients calculated at the stagnation point by using the modified newtonian theory vary with mach number and are in good agreement with those obtained from measured pressures for mach numbers from 1.2 to 6.8. At the stagnation point the theory of sibulkin, in which the diameter and conditions behind the normal shock were used, was in good agreement with the experiment when the velocity gradient at the stagnation point appropriate to the free-stream mach number was used."},
{"description":"Cortright, E.M. Aero. Eng. Rev. 15, 1956, 59. The aerodynamic problems associated with propulsion-system installations have assumed a role of vital importance in the development of supersonic aircraft. Although air-induction systems have received moderate attention in the literature, considerably less information can be found on the design and installation of turbojet exit nozzles. This condition should not be interpreted to indicate a lack of problems in jet-exit design. As flight speeds reach supersonic levels, it becomes increasingly difficult to achieve nozzle installations which are efficient over the entire speed range. The difficulties largely stem from the fact that the goals of high jet thrust and low afterbody drag are not always compatible. In many of the compromise solutions, it is generally unsatisfactory to examine isolated nozzle and afterbody performance. Rather they must be treated as a unit, and the complex effects of jet interaction with the external stream must be taken into account. To accomplish this, the nozzle and air-frame designers must closely coordinate their efforts. Some of the aerodynamic problems of nozzle afterbody combinations are outlined in this report. Particular attention is devoted to the influence of the jet-stream interaction on both nozzle thrust and after-body drag. For this purpose, use is made of shock- boundary-layer-interaction concepts. This approach, although not precise, correctly predicts many trends and is generally enlightening.","title":"Some aerodynamic considerations of nozzle afterbody combination.","url":"cran.html#doc172"},
{"description":"J. H. Gerrard University of manchester To investigate the theoretical predictions of lighthill on aerodynamic sound, measurements have been made of the sound field of a 1 in. Air jet issuing from a long pipe. The measurements have been made over a wide frequency band (30 to 10, 000 cycles/sec.) and in one-third octave bands in this frequency range. The mean mach number at the pipe orifice was varied from 0.3 to 1.0. The dependence of the apparent position of the noise sources on frequency and jet speed was investigated. At a given frequency a source is situated farther from the jet orifice the higher the jet speed. Lower frequency sources appear farther downstream than ones of higher frequency, consistent with their association with larger eddies. The directional characteristics of the sound field at different frequencies and jet speeds are illustrated by means of scale diagrams showing lines of constant sound intensity. These sound fields are analyzed in terms of the moving quadrupole sources of lighthill's theory and good agreement obtained. It is shown that the apparent spread of the sources at low frequencies is due to the doppler effect. At low frequency relative to the frequency of maximum power output) the radiation is predominantly that of three mutually orthogonal longitudinal quadrupoles which, except for the effect of convection upon it, has a sound field like a monopole source. At higher frequencies the sound fields of lateral and longitudinal quadrupoles predominate.","url":"cran.html#doc129","title":"An investigation of the noise produced by a subsonic air jet."},
{"description":"Priester, W., martin, H.A. And Kramp, K. Nature, 188, pp 200-204. 1960. Atmospheric densities have been derived from artificial satellites in altitudes 200-700 km. And From rockets up to about 200 km. To consolidate the two sets of data, H.K. Kallmann suggested a model with a exact form of this curve has now been derived. Corrections for the is excellent. Very close correlation between atmospheric density variations/h180 km./ and the solar 20-cm. Radiation implies that the origin of the'solar effect'may lie in the absorption of solar ultra-violet radiation. The atmospheric density curve between 180 and 200 km. Shows a temperature inversion in the fl-layer. It is not yet possible to decide whether solar ultra-violet radiation as well as the solar he line and solar x-ray radiation contribute to the heating of the fl-layer. Diurnal and seasonal density variations at altitudes 210, 562 and 660 km. Have been derived from variations in acceleration of three satellites/sputnik 3, vanguard 1 and 2/. Group averages of diurnal variations are taken from different dates within the period may 15, 1958-october 1, 1959. Physcal conditions in the upper atmosphere are briefly summarized..the'solar effect'originates in the fl-layer as a result of heating by the solar he line at 304 A. Diurnal density variation at 210 km. Is only a few per cent. Absorption of solar electromagnetic radiation in the f2-layer, and large heat conductivity cause intense diurnal density and temperature variations above","title":"Earth satellite observations and the upper atmosphere.","url":"cran.html#doc620"},
{"description":"Illingworth, C.R. Proc. Roy. Soc. A, 199, 1949. If the boundary-layer equations for a gas are transformed by mises's transformation, as was done by karman tsion for the flow along a flat plate of a gas with unit prandtl number, the computation of solutions is simplified, and use may be made of previously computed solutions for an incompressible fluid. For any value of the prandtl number, and any variation of the viscosity with the temperature t, after the method has been applied to flow along a flat plate (a problem otherwise treated by crocco), the flow near the forward stagnation point of a cylinder is calculated with dissipation neglected, both with the effect of gravity on the flow neglected and with this effect retained for vertical flow past a horizontal cylinder. The approximations involved by the neglect of gravity are considered generally, and the cross-drift is calculated when a horizontal stream flows past a vertical surface. When, and the boundary is heat-insulated, it is shown that the boundary-layer equations for a gas may be made identical, whatever be the main stream, with the boundary-layer equations for an incompressible fluid with a certain, determinable, main stream. The method is also applied to free convection at a flat plate variation with altitude of the state of the surrounding fluid neglected) and to laminar flow in plane wakes, but for plane jets the conditions, previously imposed by howarth, are also imposed here in order to obtain simple solutions.","url":"cran.html#doc375","title":"Steady flow in the laminar boundary layer of a gas."},
{"url":"cran.html#doc1347","title":"Approximate analysis of atmospheric entry corridors and angles.","description":"Luidens, R.W. Nasa tn.d590, 1961. A simple closed-form solution for the achievable corridor depths and entry angles as a function of g-load limit, entry velocity, and vehicle aerodynamics and thermodynamics is developed for two modes of vehicle operation, constant angle of attack and modulated angle of attack. For constant angle of attack, operation at maximum negative lift coefficient on the overshoot bound, and at an angle of attack between zero and that for maximum lift-drag ratio on the undershoot bound, gives the deepest corridor. For modulated angle of attack, operating at maximum negative lift coefficient on the overshoot bound and modulating the angle of attack from maximum positive lift coefficient to zero on the undershoot bound give the deepest corridor. The modulated angle of attack gives corridor depths two to four times larger than the fixed angle of attack. For both cases the corridor depth is increased by increasing maximum lift-drag ratio, increasing g limit, and decreasing entry velocity. Consideration of hot-gas radiation places a limit on the maximum angle of attack for either mode of operation. If a maximum free-stream reynolds number limit must be placed on the vehicle to ensure a laminar boundary layer, the deep atmospheric penetrations associated with configurations with high lift-drag ratio may be ruled out. Both of these thermodynamic considerations reduce the acceptable corridor depth below the value calculated from aerodynamic considerations alone."},
{"title":"Some considerations on the laminar stability of time-dependent basic flows.","url":"cran.html#doc1242","description":"S. F. Shen U.S. Naval ordnance laboratory As a stability criterion for infinitesimal disturbances in an incompressible, parallel but time-dependent basic flow, it is proposed to introduce the concept of /momentary stability, / which is said to prevail at the instant if the kinetic energy of the disturbances, as a fraction of the kinetic energy of the basic flow, tends to decrease. The significance of such a criterion is briefly discussed. For special time-dependent basic flows which are described by similar velocity profiles at all times (except for changes in amplitude), in the inviscid limit only a change of the time scale is needed to reduce the solution essentially to that for the steady case. The disturbances may be of either the transverse-wave or the longitudinal-vortices type. The result indicates a very strong destabilizing influence of deceleration, which is likely to overshadow that of the velocity profile under normal circumstances. The observations of fales rotating cylinders) are believed to be largely due to the deceleration. At finite reynolds numbers, the usual procedure of calculating the stability solution on the basis of the instantaneous profile is further shown to be valid only for extremely slow acceleration or deceleration. Even when the solution is acceptable, the condition for neutral stability may not be used without reservation. To calculate momentary stability properly, a procedure for a slowly varying but more general profile is also described."},
{"description":"Mark, H. Naca tm.1418. Ideally, the reflection of a shock from the closed end of a shock tube provides, for laboratory study, a quantity of stationary gas at extremely high temperature. Because of the action of viscosity, however, the flow in the real case is not one-dimensional, and a boundary layer grows in the fluid following the initial shock wave. In this paper simplifying assumptions are made to allow an analysis of the interaction of the shock reflected from the closed end with the boundary layer of the initial shock afterflow. The analysis predicts that interactions of several different types will exist in different ranges of initial shock mach number. It is shown that the cooling effect of the wall on the afterflow boundary layer accounts for the change in interaction type. An experiment is carried out which verifies the existence of the several interaction regions and shows that they are satisfactorily predicted by the theory. Along with these results, sufficient information is obtained from the experiments to make possible a model for the interaction in the most complicated case. This model is further verified by measurements made during the experiment. The case of interaction with a turbulent boundary layer is also considered. Identifying the type of interaction with the state of turbulence of the interacting boundary layer allows for an estimate of the state of turbulence of the boundary layer based on an experimental investigation of the type of interaction.","url":"cran.html#doc170","title":"The interaction of a reflected shock wave with the boundary layer in a shock tube."},
{"url":"cran.html#doc252","title":"An investigation of interference effects on similar models of different size in various transonic tunnels in the U.K..","description":"F. O/hara and L. C. Squire, R.A.E. And A. B. Haines, A.R.A. K.. Details are given of a programme of tests being made on similar swept-wing models in transonic tunnels of different types. Force measurement results at subsonic speeds in the R.A.E. 3 ft. By 3 ft. Slotted tunnel show only small interference effects for models of moderate blockage at low incidence., at higher incidences, the interference effect on lift becomes appreciably greater than estimated by theory, and significant pitching moment differences occur, apparently due to wall interference on the wing flow field. Comparable but smaller effects are evident in the results from the A.R.A. 9 ft. By 8 ft. Perforated tunnel. At speeds just above m = 1, the force fluctuates as speed is increased, because of wave reflection interference. The magnitude of the fluctuations diminishes as speed is further increased and this reduction is more marked in the perforated tunnel. Pressure measurements along the top of the body at zero incidence show delay in shock movements at high subsonic speeds indicating a blockage effect on speed., the effect is larger in the perforated tunnel though smaller than predicted by theory. Above m = 1, both expansion and shock waves are strongly reflected in the slotted tunnel but considerable alleviation, particularly of shock waves, is achieved in the perforated tunnel, for which an analysis of the effects is given, showing for example, the effect of the open-area distribution of the walls."},
{"url":"cran.html#doc1035","title":"Note on creep buckling of columns.","description":"The stability of a compressed elastic ring has been studied by a method which can be extended to solve the problem of the stability of a flexible heavy structure spread by a system of hoops as in a crinoline skirt. The original work by levy, which was developed by timoshenko and love, cannot be generalized to problems in which the compressing forces are affected by the deformation of the ring. It is shown that the load at which a ring will buckle depends not only upon the magnitude of the load but also upon its first derivative relative to the radial distance. A positive derivative causes the ring to buckle at a higher load. When this result is applied to a cone of heavy and loosely draped fabric spread by a rigid hoop of radius and a larger and flexible hoop of radius below it, both hoops being in horizontal planes, then various modes of buckling other than oval are possible according to the relative magnitudes of and. It is found that oval buckling changes to three-wave buckling when three-wave changes to four-wave when, and as and approach nearer to equality the buckled form progressively changes to more waves. When applied to a structure spread by many horizontal hoops of which the top one is rigid and oval, it is found that all other hoops, if each is designed to the criterion, will have the same absolute deviation from circularity as the rigid hoop. If any one hoop is designed so that, then the oval shape of the rigid hoop is magnified on all flexible hoops."},
{"title":"The flow past pitot tube at low reynolds numbers, part 1-dash the numerical solution of the navier-stokes equations for steady viscous axisymmetric flow, part 2-dash the effects of viscosity and orifice size on a pitot tube at low reynolds numbers.","url":"cran.html#doc1082","description":"Lester, W.G.S. O.U.E.L. No. 136, A.R.C. 22, 070, F.M. 2983. In this report numerical methods used to solve the navier-stokes equations for steady viscous two-dimensional flow are extended to include the case of axial symmetry. The equations and their finite difference approximations are derived working in cylindrical polar co-ordinates with the stokes' stream function and the vorticity as variables. A new method of dealing with the boundary conditions is given. The effects of viscosity and orlfice size on a blunt-nosed pitot tube have been theoretically investigated up to a reynolds number of ten, where the reynolds number has been based on the radius of the tube. Results are expressed in terms of a pressure coefficient where p is the pressure measured in the tube, p the density of the fluid, and p and u the static pressure and velocity in an undisturbed flow at the position of the tube. The values of c for a blunt-nosed tube are found to be less than those for tubes with hemispheroidal heads, but always greater than unity in the range considered. The effect of the orifice size is to decrease c as the orifice size increases, this decrease is very small but increases with the reynolds number. At a reynolds number of ten the decrease is at most five per cent of the value of c when there is no orifice. It is suggested that the decrease of c below unity found in some experimental investigations at a higher reynolds number could be due to the effects of orifice size."},
{"description":"Brown, W.D. And Donoughe, P.L. Naca tn.2479, 1951. The three partial differential equations of the laminar boundary layer for two-dimensional steady-state compressible flow have been transformed into two ordinary differential equations by the method of pohlhausen, falkner, and skan. The ordinary equations include parameters for expressing the simultaneous effects of pressure gradient in the main-stream flow through a porous wall and property changes in the fluid due to large temperature differences between the wall and the free stream. A total of 58 cases have been solved numerically by the method of picard. The euler number (nondimensional pressure-gradient parameter) ranges in value from 1 (stagnation-point value) to the negative values found at the laminar separation points. Three rates of flow through the porous wall were considered (including the impermeable case where the flow rate is 0). Five temperature ratios (stream temperature divided by wall temperature) were used.. The uncooled and unheated case (temperature ratio of 1), two cooled cases (temperature ratios of ture ratios of and ). Velocity, weight-flow, and temperature distributions are tabulated as are the dimensionless stream function of falkner and skan and its derivatives and the dimensionless temperature function of pohlhausen and its derivatives. For each case, displacement, momentum, and convection thicknesses, as well as nusselt number and coefficient of friction at the wall, were computed.","url":"cran.html#doc59","title":"Tables of exact laminar-boundary layer solutions when the wall is porous and fluid properties are variable."},
{"title":"Vibration isolation of aircraft power plants.","url":"cran.html#doc100","description":"Taylor, E.S. And Browne, K.A. J. Ae. Scs. 6, 1938, 43. Vibration in aircraft structure can almost always be traced to vibratory forces originating from the power plant. These forces are transmitted to the aircraft in two ways.. (1) by the action of air forces upon the surfaces of the aircraft in, or adjacent to, the slip stream of the propeller, and (2) by direct transmission of unbalanced forces from the power plant through the engine mounting. The latter has always caused the preponderance of disturbance. Vibratory stresses induced in the engine mounting structure occasionally produce fatigue failures in the associated parts, and always shorten the useful life of the entire aircraft structure. More important, however, are the psychological and physiological effects of continuous vibration and its attendant noise on the passengers and crew. This may very likely be the major source of the rapid fatigue which is so intimately associated with flying. The importance and desirability of drastically reducing vibration can hardly be questioned. This paper is limited to a consideration of the directly transmitted forces and, further, considers the power plants as rigid bodies attached by flexible means to the aircraft which is also considered as a rigid body of relatively large mass. It is also limited to the case of engines and engine supporting structures having axial symmetry (radial engines), although the methods employed could easily be extended to other cases."},
{"description":"Newson, W.A. Naca tn.4124, 1957. An investigation has been made to study the effect of ground proximity on the aerodynamic characteristics of a four-engine vertical- take-off-and-landing transport-airplane model with tilting wing and propellers. Tests were made with the wing at an angle of incidence of 90, the position used for vertical take-off or landing. With the model at various heights above the ground, the lift, drag, and pitching moment were measured and tuft studies were made to determine the flow field caused by the propeller slipstream. Data were obtained for the complete model, for the model with horizontal tail removed, and for the wing-propeller combination alone. The results of the investigation showed that, when the model was hovering near the ground, there was a strong upwash in the plane of symmetry and also an increase in lift of about 10 percent of the propeller thrust. About one-half of this lift resulted from an increase in propeller thrust and one-half resulted from an up load on the fuselage induced by the upwash. As the model approached the ground, it also experienced an increasing nose-down pitching moment that evidently resulted from the up load on the fuselage, the rear part of which was longer than the front part. The addition of the horizontal tail which was located about halfway up the vertical tail did not increase the nose-down pitching moment because the fuselage decreased the energy of the upwash before it reached the tail.","url":"cran.html#doc1164","title":"Effect of ground proximity on the aerodynamic characteristics of a four- engined vertical take-off and landing transport airplane model with tilting wing and propellers."},
{"title":"Inelastic behaviour of structures subjected to cyclic thermal and mechanical stressing conditions.","url":"cran.html#doc837","description":"Padlog, J., huff, R.D. And Holloway, G.F. Wadc tr 60-271, 1960. A general analytical procedure is outlined for structures subjected to varying thermal and mechanical stressing conditions. Consideration is given to the accumulation of time-independent plastic strains and creep strains. Stress-strain-temperature-time relations for uniaxial and multiaxial stresses are defined, based on various material behavior assumptions. Several of the assumptions are compared with a limited number of time-varying temperature and uniaxial stress tests. The procedure is illustrated by its application to uniaxial stress problems in which /planes originally plane remain plane/ and to plane stress plate problems. A solution, based on the influence coefficient approach to the plane stress plate problem, is obtained which is applicable to all plate plan forms, edge boundary conditions, and inplane thermal and mechanical loading conditions. From the predicted inelastic behavior of a three-bar structure subjected to cyclic thermal and mechanical loading conditions, it is shown that eventual failure could result from large permanent deformation accumulations, tensile rupture, or thermal-stress-fatigue. A sample plate with a centrally located hole was analyzed for two cycles of a time-varying temperature and edge stress condition. Both plastic strain reversals and plastic strain growths were predicted at the hole. However, a test-theory comparison indicated failure by creep-rupture."},
{"description":"Cresci, R.J. And Libby, P.A. J.aer.scs. 29, 1962, 815. The influence of localized mass transfer at the nose of a slender cone under hypersonic flow conditions has been studied by experimental and theoretical means. Two gaseous coolants, nitrogen and helium, are injected through a porous plug subtending a half angle of 30. The effect of the mass transfer on the shock shape, pressure distribution, heat transfer, and transition are investigated. The experimental work involved tests in the mach-number-8.0 tunnel at pibal. The theoretical analysis involved a study of the effect of mass transfer on the shock stand-off distance and leads to an inviscid-flow parameter permitting the experimentally determined shock shape and pressure distribution to be extrapolated to other than test conditions and to other coolant gases. There is obtained the maximum value of this parameter resulting in no significant alteration of the pressure distribution on the cone and thus defining the flows in which boundary-layer-type similarity applies. Significant reductions in heat transfer are obtained with injection. Indeed, with small amounts of helium injection the peak heating is found to occur downstream on the cone and to be an order of magnitude less than would occur at the stagnation point without mass transfer. With nitrogen early transition is found to occur, so that local heating rates are actually increased over those prevailing at the same reynolds number without injection.","url":"cran.html#doc123","title":"The downstream influence of mass transfer at the nose of a slender cone."},
{"url":"cran.html#doc799","title":"Some effects of wind-tunnel interference observed in tests on two-dimensional aerofoils at high subsonic and transonic speeds.","description":"Pearcey, H.H., sinnott, C.S. And Osborne, J. N.P.L. Aero. 373. February 1959. In the high-speed research on two-dimensional aerofoils at the national physical laboratory the need to keep model size above a certain minimum, in order to reproduce correctly the boundary layer separation effects experienced at full scale, has been considered paramount even at the risk of incurring significant tunnel interference effects. This report discusses the interference effects for the slotted working sections now in use. The magnitudes of the blockage and lift effect corrections are deduced for the ratio of model chord to tunnel height normally used. It is shown that a simple adaptation to reduce the open area of the walls would reduce both corrections to insignificant proportions simultaneously, but would give a reduced choking mach number separated flows. The observed trends in the variation of the blockage effects for other ratios of model chord to tunnel height differ from those predicted theoretically, and so the results cannot be applied more generally until these trends have been checked by further investigations. It is suggested that wake interference effects can significantly influence the manner in which separated flows develop with increasing incidence or mach number, particularly for walls of small open area. Examples are also given of effects of distortions in the local supersonic flow, which are most noticeable for walls with relatively large open areas."},
{"description":"Diaz, G.B., and greenberg, H.G. J. Math. Phys. 27, 1948, 193. Let w(x, y) be a solution of the boundary value problem where r is a plane domain with the boundary C. The authors obtain upper and lower bounds for, the value of w at a point in r, by a method which is applicable to many other problems. If u is a function satisfying the boundary conditions and v is a function satisfying the partial differential equation, then the authors obtain by applying green's classical identity and schwarz's inequality a pair of inequalities of the form where. Together with the function w the authors consider a function the solution of the boundary value problem on c, and in analogy with the functions u and v associated with the function w a pair of functions and associated with the function. In the expression for derived from green's classical identity appears an unknown line integral containing the values of w and on C. But the same line integral appears also in the expressions for to which the above inequalities are applicable. In this way the authors obtain two inequalities of the form where b and b', respectively, are approximate values of. In order to improve these bounds one may add to u a linear set of functions and to v a linear set of functions and then minimize h(u-v) in order to determine the coefficients of the best linear combinations. If the sequences and are complete in a certain sense defined by the authors the approximations will converge to the value.","title":"Upper and lower bounds for the solution of the first biharmonic boundary value problem.","url":"cran.html#doc731"},
{"url":"cran.html#doc369","title":"An approximate solution of the supersonic blunt body problem for prescribed arbitrary axisymmetric shapes.","description":"Traugott, S. J. Ae. Scs. 27, 1960, 361. The integral method of belotserkovskii has been carried out to the first approximation for arbitrary blunt axisymmetric bodies in supersonic or hypersonic flight. This method is direct, in that it gives the surface-pressure distribution and shock shape for a prescribed body. Results obtained by numerical integration for several body shapes at several mach numbers are compared to experimental results with good agreement. It is also shown that the method can be successfully applied to pointed bodies with attached shock. In the stagnation region, simple relationships are found from the equations of the first approximation which connect the surface-velocity gradient, shock curvature, shock-detachment distance, and body curvature. These relations are also correlated with experiment for a variety of shapes as a function of mach number. The correlations permit a rapid estimate of the stagnation-point velocity gradient, important for heat-transfer calculations, for any blunt body from the shock stand-off distance. A method for a higher approximation is described, for which, in contrast to the higher approximations of belotserkovskii, a large number of simultaneous total differential equations with unknown parameters does not occur. One form of this method has been studied numerically. Results are given which, though only partially successful, indicate the amount of improvement to be expected from a higher approximation."},
{"description":"Onat, E.T. And Drucker, D.C. J. Ae. Scs. 20, 1953, 181. A most troublesome paradox has existed for a number of years with respect to buckling in the plastic range. Theoretical considerations and all direct experimental evidence show conclusively that an incremental or flow type of mathematical theory of plasticity is valid. However, the results of plastic buckling tests are well correlated by a simple total or deformation theory and bear no resemblance to published predictions of incremental theory. The suggestion was made that initial imperfections of shape or loading might well explain this most peculiar result. However, subsequent investigations by several authors seem to have given the impression that excessively large imperfections would be needed and that the answer would be overly sensitive to the magnitude of such imperfections. It is the purpose of this paper to demonstrate that extremely small, and therefore unavoidable, imperfections of shape do account for the paradox in a simple manner. The buckling load is shown to be extremely insensitive to the amount of imperfection. The example chosen is a simplified version of the long rectangular plate hinged along one edge and free on the other under uniform compressive stress at the ends. This is the equivalent of the case of the cruciform column, which has been so disturbing in the past because incremental theory applied to a perfect cruciform column did lead to an entirely incorrect result.","url":"cran.html#doc825","title":"Inelastic instability and incremental theories of plasticity."},
{"description":"Adams, E.W. Heat transfer and fluid mech. Inst. 1961, 222. The transient performance of ablation type heat protection shields is treated herein for the surface of a vehicle returning from outer space to the earth. The vehicle weighs 8640 kg, has a ballistic factor of 500 lb ft, re-enters with a speed of 11 km sec at ratio of 0.5, and is subjected to a maximum deceleration of 7.7 times the gravity constant. By use of well known equations for the heat transfer and the mass transfer at a heated surface, a numerical calculation method is derived which, for the investigated ablation processes, yields exact transient solutions of the fundamental system of partial differential equations. The method is applied to various quartz shields and to one teflon shield, which all evaporate so readily under the conditions of the problem at hand that practically no flow of molten shield material exists. The solutions also show comparatively small temperature changes parallel to the surface. The results show that the nose of the vehicle is cooled predominantly by the evaporation of the quartz or the teflon,. The rest of the vehicle's surface is cooled by radiation of the quartz or evaporation of the teflon. The large mass transfer effects on the nose of the vehicle are detrimental since the resulting low surface temperatures prevent the radiative heat transfer out of the shield, which does not involve any mass loss, from being the desirable governing cooling factor.","title":"Analysis of quartz and teflon shields for a particular re-entry mission.","url":"cran.html#doc274"},
{"url":"cran.html#doc157","title":"The hodographic transformation in transonic flow.","description":"Lighthill, M.J. Proc. Roy.S. A, 191, 1947, 323. The author studies the problem of finding the shape of a symmetrical nozzle with the velocity along the axis (x-axis) specified. The velocity along each streamline is assumed to increase steadily. The singularity at the sonic velocity and to the axis of the nozzle) is first studied in the physical plane by using a power series in. In the hodograph plane, the two characteristics of the hodograph differential equation passing through the sonic point and are lines of branch points. The region between these lines is a region of triple-valuedness for the stream function. Outside this region is single-valued. There are also singularities at the sonic point and the point corresponding to the specified condition at the exit of the nozzle. The author then proposes to construct in the hodograph plane by at the exit velocity and (3) a finite sum regular throughout.. Sin, where r is the square of the velocity and the are hypergeometric functions. The a's are fixed by the required approximation to the specified velocity distribution along the axis. This solution is single-valued, convergent and represents except a region near the sonic point in the nozzle. For this excluded region, the author inverts the solution to obtain a power series in for 0. This is shown to be convergent for the region of interest. The type of solution considered by the author gives a nozzle having an infinitely long supersonic part."},
{"description":"Freeman, N. C. J. Fluid mech. V. 4, 1958. The theory of an'ideal dissociating'gas developed by lighthill/1957/for conditions of thermodynamic equilibrium is extended to non-equilibrium conditions by postulating a simple rate equation for the dissociation process/including the effects of recombination/. This equation contains the'equilibrium'parameters of the lighthill theory plus a further dissociation phenomena. The behaviour of this gas is investigated in flow through a strong normal shock wave and past a bluff body. The assumption is made that the gas receives complete excitation of its rotational and vibrational degrees of freedom in an infinitesimally thin region according to the familiar rankine-hugoniot shock wave relations before dissociation begins. The variation of the relevant thermodynamic variables down-stream of this region is then computed in a few particular cases. The method used in the latter case is an extension of the'newtonian'theory of hypersonic inviscid flow. In particular, the case of a sphere is treated in some detail. The variation of the shock shape and the sphere diameter to the length scale of the dissociation process, is exhibited for conditions extending from completely undissociated flow to dissociated flow in thermal equilibrium. Results would indicate that significant and observable changes from the undissociated values occur, although values for the non-equilibrium parameter are not, at present, available.","url":"cran.html#doc317","title":"Non-equilibrium flow of an ideal dissociating gas."},
{"description":"Conti, R.J. Nasa tn.d962, 1961. Two circular conical configurations having 15 half-angles were tested in laminar boundary layer at a mach number of 6 and angles of attack up to 90. One cone had a sharp nose and a fineness ratio of blunted nose with a bluntness ratio of 0.1428 and a fineness ratio of 1.66. Pressure measurements and schlieren pictures of the flow showed that near-conical flow existed up to an angle of attack of approximately near the base and the bow shock wave was considerably curved. Comparison of the results with simply applied theories showed that on the stagnation line pressures may be predicted by newtonian theory, and heat transfer by local yawed-cylinder theory based on the yaw angle of the windward generator and the local radius of the cone. Base effects increased the heat transfer in a region extending forward approximately circumferential pressure distributions were higher than the corresponding newtonian distribution and a better prediction was obtained by modifying the theory to match the pressure at 90 from the windward generator to that on the surface of the cone at an angle of attack of 0. Circumferential heat-transfer distributions were predicted satisfactorily up to about 60 from the stagnation line by using lees' heat-flux distribution based on the newtonian pressure. The effects of nose bluntness at large angles of attack were very small in the region beyond two nose radii from the point of tangency.","title":"Laminar heat-transfer and pressure measurements at a mach number of 6 on sharp and blunt 15 half-angle cones at angles of attack up to 90.","url":"cran.html#doc1307"},
{"title":"Aerodynamic investigation of a parabolic body of revolution at mach number of 1. 92 and some effects of an annular supersonic jet exhausting from the base.","url":"cran.html#doc1352","description":"Love, E.S. Naca tn.3709, 1956. 92 and some effects of an annular supersonic jet exhausting from the base. An aerodynamic investigation of a parabolic body of revolution was conducted at a mach number of 1.92 with and without an annular supersonic jet exhausting from the base. Measurements with the jet inoperative were made of lift, drag, pitching moment, radial and longitudinal pressure distributions, and base pressures. With the jet in operation, measurements were made of the pressures over the rear of the body with the primary variables being angle of attack, ratio of jet velocity to freestream velocity, and ratio of jet pressure to stream pressure. The results with the jet inoperative showed that the radial pressures over the body varied appreciably from the distribution generally employed in most approximate theories. The linearized solutions for lift, pitching moment, and center of pressure gave relatively poor predictions of the experimental results. An analysis of several theoretical methods for calculating pressure distribution and wave drag showed that some methods gave results in considerable disagreement with experimental values. Maximum effects of the jet were obtained at the lower ratio of jet velocity to stream velocity and the highest ratio of jet pressure to stream pressure. These effects amounted to a slight decrease in fore-drag, a reduction in lift, and a shift of center of pressure in a destabilizing direction."},
{"description":"Ribner, H.S. Utia r37, 1956. At high speeds the turbulent boundary layer washing the airplane fuselage excites appreciable skin vibration, promoting strong noise in the interior. The fluctuating exciting pressure distribution can be represented as a pattern of moving waves (fourier integral). A running ripple in the skin follows underneath each wave, and the noise is ultimately due to these ripples. The acoustic effects of the running ripples are calculated for an infinite sheet,. This is considered the main result of the paper. Supersonically moving ripples radiate strong sound in the form of mach waves,. Subsonically moving ripples radiate no sound. Formulas for the mean square surface pressure and the energy flux are obtained for an assumed idealized turbulent pressure spectrum. The results are adapted to provide a tentative estimate of the noise generated at subsonic speeds in a practical fuselage. The running ripples are almost noise-free, but multiple reflections at the frames and stringers promote standing waves. An assumption is used to link the two kinds of waves, and this leads to provisional calculations of noise level.. On this basis the noise level is predicted to vary as for thin boundary layers, changing progressively to for thick layers ( = external air density, = speed, = layer thickness, = panel thickness). Some comparisons are made with experiment. Finally, an idea for minimizing the noise is presented.","title":"Boundary layer induced noise in the interior of aircraft.","url":"cran.html#doc209"},
{"title":"Effect of diffusion fields on the laminar boundary layer.","url":"cran.html#doc342","description":"Smith, J.W. J.ze.scs. 21, 1954. A theory is developed which describes the effect of a general diffusion field on the dynamic and thermal characteristics of a laminar boundary layer on a flat plate in steady compressible flow. Fluid properties are considered as functions of temperature and local concentration of the foreign gas. The diffusion field is described by a differential equation that relates convective and diffusion transfer and which considers diffusion currents arising from gradients of concentration and temperature. By means of the usual transformations the system is reduced to a set of ordinary differential equations, which in turn are transformed into a set of integral equations. The latter is amenable to solution by the method of successive approximations. The theory and results have bearing on the problem of control and reduction of aerodynamic heating at hypersonic speeds. The special feature of this approach lies in the utilization of diffusion fields for the purpose of reducing the detrimental effects of viscous dissipation. Although the theory is adapted to a fuller investigation of this problem, the numerical examples considered involve mainly diffusion fields of helium, with which good results have been achieved at mach numbers 8 and 12. Whereas at the higher mach number the influx of heat was practically eliminated, a reversal in the direction of heat flow has been effected at the lower mach number."},
{"description":"Wray, K.L. Hypersonic flow research, p 181, academic press, new york, 1962. When a hypersonic object enters earth's atmosphere, a shock wave is formed in front of it, and the air passing through this shock wave is heated to high temperatures. The shock heated molecules equilibrate their translational and rotational degrees of freedom within a distance of a few mean free paths. To achieve equilibrium, it is necessary to excite vibration, dissociate molecules, produce new molecules and produce ions and electrons. The problem is complex, since all these phenomena occur simultaneously and because the reaction rates depend on the temperature, density and composition which are changing during the relaxation toward equilibrium. The experimental techniques used to investigate these reactions are briefly discussed along with the resulting rate expressions obtained by the various investigators. A compilation of the rate expressions for these reactions representing the author's evaluation of all the available data is presented. Several pertinent problems which are not yet completely understood and which still require theoretical and experimental investigation are outlined. Computed concentration, temperature and density time histories are shown for three different shock speeds in air. The time rate of change of concentration for each chemical reaction is also shown and regimes of importance for the various processes are discussed.","url":"cran.html#doc552","title":"Chemical kinetics of high temperature air."},
{"url":"cran.html#doc1333","title":"Aerodynamic forces on wings in non-uniform motion.","description":"Jones, W.P. Arc r + M.2117, 1945. The problem of determining the aerodynamic forces acting on wings of finite span in non-uniform motion in an incompressible, inviscid fluid is investigated. The underlying theory is outlined in 2, and some known results for the case of an aerofoil of infinite span are included in 3. It is shown in 4, by the use of operational methods, that the growth of lift function k (s) corresponding to a sudden unit change of incidence can be derived from the lift function corresponding to simple harmonic translational motion. From results given by the writer for rectangular wings (1943) and tapered wings (1945) in simple harmonic motion the corresponding values of k (s) are determined. The growth of lift function k (s) for a wing penetrating a uniform vertical gust can then be estimated as shown in 4 and 5. By the use of approximate formulae for the growth of lift curves given in fig. 2, the aerodynamic forces corresponding to damped and growing translational oscillations are derived. Certain integrals involved in the theory are evaluated in appendix 1, and in appendix 2 the method of determining k (s), when k (s) is known, is discussed in detail. It is suggested that the aerodynamic forces acting on wings of finite span for any type of motion can best be derived from a knowledge of the forces corresponding to purely divergent motion, which can be calculated by the methods outlined in this report."},
{"url":"cran.html#doc476","title":"The blasius equation with three-point boundary conditions.","description":"Napolitano, I. G. Quart. Appl. Math. V. 16, no. 4, pp 397-408, 1958. The blasius equation subject to three-point boundary conditions, describing the interaction between two parallel streams, is solved by way of a series in terms of ascending powers of the ratio equals /u1 -dash u2//u1, where the u1's are the outer streams' velocities. The first three terms of the series are analytically expressed in terms of the repeated integrals of the complementary error function /im erfc / and of the repeated integrals of the square of the successive integrals of the complementary error function /jmin erfc n/. These functions often appear in problems leading to extended heat-conduction type of equations. A recurrence formula for jmin erfc n is established and formulae relating the functions in erfc /-dashn/ and jmjn erfc to available tabulated values of the functions in erfc /n/ are derived. The first three approximations to the blasius function and to its first two derivatives are also presented in tabulated form with four significant figures. Test on the convergence of the series has been made by comparison with some exact solutions obtained by high speed computing machine. The comparison, extended to the physically essential quantities, shows that.. Second and first derivatives. Yield extremely accurate results. The errors in the first two derivatives of the blasius functions are always contained within less than one per cent."},
{"description":"Cohen, D. Naca R.1050, 1951. The method of superposition of linearized conical flows has been applied to the calculation of the aerodynamic properties, in supersonic flight, of thin flat, swept-back wings at an angle of attack. The wings are assumed to have rectilinear plan forms, with tips parallel to the stream, and to taper in the conventional sense. The investigation covers the moderately supersonic speed range where the mach lines from the leading-edge apex lie ahead of the wing. The trailing edge may lie ahead of or behind the mach lines from its apex. The case in which the mach cone from one tip intersects the other tip is not treated. Formulas are obtained for the load distribution, the total lift, and the drag due to lift. For the cases in which the trailing edge is outside the mach cone from its apex (supersonic trailing edge), the formulas are complete. For the wing with both leading and trailing edges behind their respective mach lines, a degree of approximation is necessary. It has been found possible to give practical formulas which permit the total lift and drag to be calculated to within 2 or 3 percent of the accurate linearized-theory value. The local lift can be determined accurately over most of the wing, but the trailing-edge-tip region is treated only approximately. Charts of some of the functions derived are included to facilitate computing, and several examples are worked out in outline.","title":"Formulas for the supersonic loading, lift and drag of flat swept back wings with leading edges behind the mach lines.","url":"cran.html#doc1343"},
{"description":"Spreiter, J.R. And Sacks, A.H. Naca r1296, 1957. A theoretical study is made of some cruciform-wing arrangements and their wakes by means of slender-body theory. The basic ideas of this theory are reviewed and equations are developed for the pressures, loadings, and forces on slender cruciform wings and wing-body combinations. The rolling-up of the vortex sheet behind a slender cruciform wing is considered at length and a numerical analysis is carried out using 40 vortices to calculate the wake shape at various distances behind an equal-span cruciform wing at 45 bank. Analytical expressions are developed for the corresponding positions of the rolled-up vortex sheets using a 4-vortex approximation to the wake, and these positions are compared with the positions of the centroids of vorticity resulting from the numerical analysis. The agreement is found to be remarkably good at all distances behind the wing. Photographs of the wake as observed in a water tank are presented for various distances behind a cruciform wing at 0 and 45 bank. For 45 bank, the distance behind the wing at which the upper two vortices pass between the lower two is measured experimentally and is found to agree well with the the calculation of loads on cruciform tails is considered in some detail by the method of reverse flow, and equations are developed for the tail loads in terms of the vortex positions calculated in the earlier analyses.","title":"A theoretical study of the aerodynamics of slender cruciform-wing arrangements and their wakes.","url":"cran.html#doc289"},
{"url":"cran.html#doc656","title":"Departure from dissociation equilibrium in a hypersonic nozzle.","description":"Bray, K.N.C. A.R.C. 19, 983, march 1958. The equations of motion for the flow of an ideal dissociating gas through a nearly conical nozzle have been solved numerically, assuming a simple equation for the rate of dissociation, and a number of different values of the rate constant. The results of these calculations suggest that deviations from dissociation equilibrium will occur in the nozzle if the rate constant lies within a very wide range of values. They also suggest that once such a deviation has begun the gas will very rapidly/freeze/, so that the dissociation fraction will remain almost constant if the flow is expanded further, or even if it passes through a constant area test section. An approximate method of solution, making use of this property of sudden/freezing/of the flow, has been developed and applied to the problem of estimating the deviations from equilibrium under a wide range of conditions. If all the assumptions made in this report are accepted, then lack of dissociation equilibrium may be expected in the working sections of hypersonic wind tunnels and hypersonic shock tubes. It is shown, however, that the flow behind a normal shock wave in such a wind tunnel will not be greatly affected by any freezing that may take place in the nozzle upstream of the shock wave. Even so, the stand-off distance of a shock wave in front of a blunt model may be quite sensitive to deviations from equilibrium."},
{"url":"cran.html#doc232","title":"Accuracy of approximate methods for predicting pressure on pointed non-lifting bodies of revolution in supersonic flow.","description":"Ehret, D.M. Naca tn.2764. The accuracy and range of applicability of the linearized theory, second-order theory, tangent-cone method, conical-shock-expansion theory and newtonian theory for predicting pressure distributions on pointed bodies of revolution at zero angle of attack are investigated. Pressure distributions and integrated pressure drag obtained by these methods are compared with standard values obtained by the method of characteristics and the theory of taylor and maccoll. Three shapes, cone, ogive, and a modified optimum body, are investigated over a wide range of fineness ratios and mach numbers. It is found that the linearized theory is accurate only at low values of the hypersonic similarity parameter number to body fineness ratio) and that second-order theory appreciably extends the range of accurate application. The second-order theory gives good results on ogives when the ratio of the tangent of maximum surface angle to the tangent of the mach angle is less than 0.9. Tangent-cone method cannot be widely applied with good accuracy. In general, the conical-shock-expansion theory predicts pressure and drag within engineering accuracy when the hypersonic similarity parameter is greater than 1.2. Although newtonian theory gives good accuracy, except for cones, at the highest values of the hypersonic similarity parameter investigated, it is less accurate than the conical-shock-expansion theory."},
{"title":"Influence of the leading-edge shock wave on the laminar boundary layer at hypersonic speeds.","url":"cran.html#doc334","description":"Lester lees California institute of technology In order to bring out the importance of the leading-edge region at hypersonic speeds, the influence of the leading-edge shock wave on the laminar boundary layer is investigated in two simple cases of steady flow over a semi-infinite, insulated flat plate.. (1) sharp leading edge., (2) blunt leading edge, as approximated by a normal shock wave. The streamlines that enter the boundary layer over a large region of the plate surface has previously crossed the shock wave very near the leading-edge, where the shock is strong and highly curved. Consequently, the temperature at the outer edge of the boundary layer is appreciably higher than free-stream temperature, and the vorticity there is not zero. The effects of this shock-wave larger than the usual /errors/ made in the boundary-layer theory, and an estimate of these effects can therefore be obtained within the framework of that theory. The numerical magnitude of the shock-wave influence is found to be appreciable. For the case of the blunt leading edge the slope of the curve of induced pressures plotted against the hypersonic interaction parameter closely approaches the experimental data of hammitt and bogdonoff obtained in helium at large values of this parameter. These approximate results show that the influence of the leading-edge region at hypersonic speeds requires careful theoretical and experimental study."},
{"description":"Clouston, J.G., gaydon, A.G. And Hurle, I.r Proc. Roy. Soc. A252, p143, september 1959. The sodium-line reversal method, as previously described, using a photomultiplier and oscillograph, has been modified. Two light beams are now employed, and interference filters are used in front of the photomultipliers instead of a spectrograph. In one beam the background source is viewed directly, through the shock tube, and in the other beam the background source is viewed through the shock tube by a mirror system with a neutral filter interposed to reduce its effective brightness temperature. With a suitably chosen temperature for the background, one oscillograph trace indicates absorption and the other indicates emission of the sodium lines. It is thus possible, from the records of a single shock, to determine the temperature history behind the shock wave to about 20degreec. Nitrogen and oxygen again show relaxation effects near the front. Temperatures in argon tend to come low, owing to radiative disequilibrium,. Excitation processes in argon are discussed. With this system it is possible to determine temperatures rather higher than that of the background source. Some work has also been done, with a single-beam method, using a carbon arc as background and following reversal of the indium blue line. Temperatures up to 3600degreek have been measured in shocks through nitrogen, but the time resolution is not so good.","title":"Temperature measurements of shock-waves by spectrum-line reversal, ii a double beam method.","url":"cran.html#doc1316"},
{"description":"Nonweiler, T.R.F. Arc, 22670, march 1961. An appropriate form of the boundary layer stability equation is developed for the condition where the fluid is in contact with an isotropic and homogeneous elastic medium, and various approximate analytical solutions obtained for certain types of surface, so as to reveal at least qualitatively the origin and characteristics of neutral oscillations. In the worked solutions the elastic medium is treated as nondissipative, and the interior boundary is supposed either fixed, or free of stress, or exposed to fluid.. The boundary layer, also, is treated as that over a flat-plate in an incompressible fluid. The results obtained show that the presence of such a resiliant surface introduces the possibility of a number of other modes of oscillation schlichting waves. Most of these modes have speeds of propagation determined largely by the properties of the elastic material, and their presence may well be effectively a matter of 'non-viscous' flow stability -dash a subject not treated here. The tollmien-schlichting mode has its minimum reynolds number increased by the presence of the surface, but if the interior boundary is free there may be an upper limit as well. Indeed, a sufficiently thin free surface, or one of low rigidity, apparently eliminates neutral oscillations of this mode altogether, only at the expense, however, of the introduction of a mode of flexural waves.","title":"Qualitiative solutions of the stability equation for a boundary layer in contact with various forms of flexible surface.","url":"cran.html#doc1322"},
{"url":"cran.html#doc589","title":"Some stall and surge phenomena in axial flow compressors.","description":"Observations of rotating stall have shown that a wide variety of stall patterns is possible. Hot-wire anemometer data on a multistage compressor have shown a progressive-type stall at low speeds. The amplitude of the flow fluctuations increases in magnitude through the first few stages and then diminishes rapidly to a small value in the latter stages. A stage-stacking analysis has shown that rotating stall will exist over a large portion of the compressor map at low speeds but will be instigated almost simultaneously with compressor surge at high speeds. Blades failures attributable to resonant vibrations excited by rotating stall have been experienced in single and multistage compressors. In the stage-stacking analysis no deterioration of stage performance due to unsteady flow resulting from stall of adjacent stages was considered. In general, the pressure drop at the stall point is believed to be much larger than indicated by an analytical formulation of compressor performance. Compressor surge is attributed to a limit cycle operation about the compressor stall point, and, as indicated in a few compressor tests and in jet-engine tests, a small compressor discharge receiver volume may result simply in stall of the compressor without the cyclic characteristics of compressor surge. In this event, engine operation will be limited because of the large drop in performance which accompanies compressor stall."},
{"description":"Goddard, F.E. J. Ae. Scs. 1959, 1. An experimental program was carried out in the 18-in. By 20-in. Supersonic wind tunnel of the jet propulsion laboratory to determine the effect of uniformly distributed sand-grain roughness on the skin-friction drag of a body of revolution for the case of a turbulent boundary layer. The mach number range covered was 1.98 to 4.54, and the reynolds number varied from about 3 x 10 to 8 x 10. Some data were also obtained at a mach number of 0.70. At speeds up to a mach number of 5 and for roughness sizes such that the quadratic resistance law holds, the compressibility effect is indirect, and the skin-friction drag is a function of only the roughness reynolds number, exactly as in the incompressible case. It is shown that the entire compressibility effect is a reduction of the fluid density at the surface as the mach number increases. The critical roughness, below which the surface is hydraulically smooth, is,. This is equal to the thickness of the laminar sublayer for a smooth surface for both compressible and incompressible flow. Over the range of roughness sizes considered here, there appears to be no wave drag associated with the drag due to roughness. The shift in the turbulent veocity profile for a rough surface at supersonic speeds is a function of only the roughness reynolds number and quantitatively follows exactly the same law as that for the incompressible case.","title":"Effect of uniformly distributed roughness on turbulent skin-friction drag at supersonic speeds.","url":"cran.html#doc1212"},
{"description":"Dean R. Chapman application to turbulent separations is made for a prandtl number of Naca technote 3792 unity in low-speed flow without injection. All calculations are for the case of zero boundary-layer thickness at the position of separation. For alminar separations the differential equations for viscous flow at arbitrary mach number are solved for the enthalpy and velocity profiles within the thin layer where mixing with dead air takes place. Results are presented in tabular form for prandtl numbers between 0.1 and 10. The rate of heat transfer to a separated laminar region in air laminar boundary layer having the same constant pressure. Injection of gas into the separated region is calculated to have a powerful effect in reducing the rate of heat transfn to the wall. It is calculated that a moderate quantity of gas injection reduces to zero the heat transfer in a laminar separated flow. The flow field analyzed consists of a thin, constant pressure viscous mixing layer separated from a solid surface by an enclosed region of low-velocity air (/dead air/). The law of conservation of energy is employed to relate calculated conditions within the separated mixing layer to the rate of heat transfer at the solid surface. This physical speed is app ied to alminar separations in compressible flow for various prandtl numbers, including consideration of the case where air is injected into the separated region.","title":"A theoretical analysis of heat transfer in regions of separated flow.","url":"cran.html#doc240"},
{"description":"Queiijo, M.J. And Riley, D.R. Naca, tn 3245, 1954. Subsonic span loads and the resulting stability derivatives have been calculated for a systematic series of vertical- and horizontal-tail combinations in sideslip and in steady roll in order to provide information embracing a wide range of probable tail configurations. All calculations were made by application of the discrete-horseshoe-vortex method to the problem of estimating loads on intersecting surfaces. The investigation covered variations in vertical-tail aspect ratio, the ratio of horizontal-tail aspect ratio to vertical-tail aspect ratio, the effects of horizontal-tail dihedral angle /for the sideslip case/, and the effects of vertical position of the horizontal tail for surfaces having their quarter-chord lines swept back 0degrees and 45degrees. The results of the investigation are presented in charts from which the span loads for the various conditions can be obtained. The resulting stability derivatives are presented as vertical- and horizontal-tail contributions as well as total-tail-assembly derivatives. The results of this investigation, which was made for a wider range of geometric variables than previous studies, showed trends which were in general agreement with the results of previous investigations. Also presented in this paper and used in the computations is an extensive table of values of sidewash due to a rectangular vortex.","url":"cran.html#doc782","title":"Calculated subsonic span loads and resulting stability derivatives of unswept and 45degree sweptback tail surfaces in sideslip and steady roll."},
{"description":"Crocco, L. And Lees, L. J. Ae. Scs. 19, 1952, 649. By means of a simplified theoretical /model, / the present paper treats the general class of flow problems characterized by the interaction between a viscous or dissipative flow near the surface of a solid body, or in its wake, and an /outer/ nearly isentropic stream. For the present, the external flow is taken to be a plane, steady, supersonic flow, which makes a small angle with a plane surface or plane of symmetry, although the methods used can be extended to curved surfaces, to axially symmetric supersonic flows, and also to subsonic flows. The internal dissipative flow is regarded as quasi-one-dimensional and parallel to the surface on the average, with a properly defined mean velocity and mean temperature. The nonuniformity of the actual velocity distribution is taken into account only approximately by means of a relation between mean temperature and mean velocity. Mixing, or the transport of momentum from outer stream to dissipative flow, is considered to be the fundamental physical process determining the pressure rise that can be supported by the flow. With the aid of this concept, a large number of flow problems is shown to be basically similar, such as boundary-layer shockwave interaction, wake flow behind blunt-based bodies (base pressure problem), flow separation in overexpanded supersonic nozzles, separation on wings and bodies, etc.","title":"A mixing theory for the interaction between dissipative flows and nearly isentropic streams.","url":"cran.html#doc97"},
{"title":"On the vibration of thin cylindrical shells under internal pressure.","url":"cran.html#doc846","description":"Fung, Y.C., sechler, E.E. And Kaplan, A. J. Ae. Scs. 27, 1957, 650. The frequency spectra and vibration modes of thin-walled circular cylinders subjected to internal pressure are considered. It is shown that for very thin cylinders the internal pressure has a significant effect on the natural vibration characteristics. For these cylinders, particularly those having smaller length to diameter ratios, the mode associated with the lowest frequency is in general not the simplest mode. The exact number of circumferential nodes, n, which occur in the mode associated with the lowest frequency, depends on the internal pressure P. If this number n is large, it decreases rapidly with increasing p when p is small, and the /fundamental/ frequency--the lowest frequency at each p--increases rapidly with increasing internal pressure. At higher values of internal pressure the frequency spectrum tends to be arranged in the regular manner, the frequency increases with the increasing number of circumferential nodes, and the lowest frequency rises slowly with the internal pressure. Experimental results on the frequency spectra, vibration modes, and structural damping of a series of thin-walled cylinders subjected to internal pressure are briefly described. These results show agreement with the features predicted by reissner's the effect of slight deviation of the cylinder from perfect circular symmetry is discussed."},
{"description":"Lighthill, M.J. J. Fluid mech. 9, 1960, 465. Most treatments of magnetohydrodynamic waves have confined physical interpretation to cases when the alfven velocity a is small compared with the sound velocity A. Here we consider the 'low-beta situation', in which a is much larger than A. Then, except for two modes with wave velocity a the only possible waves are longitudinal ones, propagated unidirectionally along lines of magnetic force with velocity A. These can be interpreted as sound waves, confined to effectively rigid magnetic tubes of force. Hall-current effects do not alter these conclusions (in contrast to the high-beta situation), and finite conductivity introduces only small dissipation. An application is made to the flow pattern around a body moving through the f layer of the ionosphere, where, although neutral particles have a very large mean free path, charged particles interact electrostatically and, it is argued, may be regarded as forming a continuous fluid whose movement is independent of that of the neutral particles. A body moving at satellite speed or below would then excite the above-mentioned unidirectional sound waves, but no waves at much faster alfven velocity. These considerations suggest that its movement would be accompanied by a v-shaped pattern of electron density (figure 2), which might be in part responsible for some anomalous radar echoes that have been reported.","title":"Notes on waves through gases at pressures small compared with the magnetic pressure, with applications to upper atmosphere aerodynamics.","url":"cran.html#doc296"},
{"url":"cran.html#doc138","title":"Wakes in axial compressors.","description":"Pearson, H. And Mckenzie, A.B. J.roy.ae.S.63, 1959, 415. The tendency in the past has been to assume that when wakes or non-uniform total head profiles are fed into an axial compressor then substantially constant static pressure prevails at the entry, the variations in total head appearing as variations in velocity. This variation in velocity causes variation in incidence on the early stage blade rows and thus can give rise to excitation of blade vibration. This assumption is implicit, for instance, in references 1 and 2, but we think has been a common assumption by most of the people working in this field. Where the compressor is fed by a duct of substantially parallel walls for a reasonable length ahead, such an assumption appeared justifiable. Such a duct when given an air flow test with its outlet discharging, for instance, to atmosphere instead of to the compressor, then the distribution assumed would normally be obtained and in fact many surveys of such ducts have been represented in this fashion. The object of this note is to show that, in fact, this distribution will not normally occur when the compressor is present and we may normally expect much more nearly a constant velocity into the compressor with attendant static pressure distributions to match with the total head variations ahead of the intake, with of course, the attendant curved flow to support the static pressure gradients."},
{"description":"Strand, T. J. Ae. Scs. 29, 1962, 702. The performance theory for high-speed air-cushion vehicles operating in close proximity to the ground is developed. The analysis is restricted to cruise flight of vehicles of rectangular planform employing an air pressure seal between the ground and the vehicle along the two streamwise sides. The variation of the optimum rearward deflection angle of the side jet pressure seal with speed for minimum overall power expenditure and maximum range is found. It is concluded that a mixed propulsion system (jet deflection plus propeller(s)) is required. Volume flow and the corresponding fan pressure rise needed are also calculated. The maximum lift drag ratio is determined. The maximum thickness ratios of the vehicles are considered to be large compared with the ground-height vehicle-length ratio. Two-dimensional airfoil theory is employed to show that close to stagnation conditions exist below the vehicles. The lower-surface lift, pitching moment, and aerodynamic-center location are determined. The flow over the upper surface is identified with flow over mounds. Upper-surface lift coefficients are determined for typical mound shapes. It is shown that high total lift coefficients are theoretically obtainable with almost zero induced drag. The conventional induced-drag power penalty is replaced by a sealing-air power expenditure, which is shown not to be excessive.","title":"Cruise performance of channel-flow ground effect machines.","url":"cran.html#doc624"},
{"description":"Levy, S. J.ae.scs. 19, 1952. Numerical computations have been performed for the boundary-layer form of the energy equation for incompressible flows with power-function variation of free-stream velocity (u = cx) and of wall temperature (t = ax), the pertinent solutions of the momentum equation in this case being those of hartree. The numerical computations given herein are to some extent a repetition of those given by schuh and by chapman and rubesin, the object of the present computations being the resolution of discrepancies appearing in the previous solutions and an extension of their range. Ibm machine calculations were employed in the finite difference calculation presently utilized, the results thereof covering a range of wall-temperature function exponents from values of m(4, 1, 0, -0.0904). The accuracy of the numerical computations is examined in detail, and the accuracy of the computed functions at the wall, which determine the heat-transfer rate, is estimated to be within 2 per cent. Examination of the results reveals that the results of schuh for the flat plate are in error. For the range of the calculations, it was found that the local heat-transfer coefficient can, with the exception of large negative values, be expressed within 5 per cent as where the exponent of the prandtl number varies from 0.254 to 0.367 for -0.0904 and where the function can be approximated by the equation","title":"Heat transfer to constant property laminar boundary layer flows with power function free stream velocity and wall temperature variation.","url":"cran.html#doc325"},
{"description":"Vonkarman, T. And Millikan, C.B. Naca R.504, 1934. The paper presents a mathematical discussion of the laminar boundary layer, which was developed with a view of facilitating the investigation of those boundary layers in particular for which the phenomenon of separation occurs. The treatment starts with a slight modification of the form of the boundary layer equation first published by von mises. Two approximate solutions of this equation are found, one of which is exact at the outer edge of the boundary layer while the other is exact at the wall. The final solution is obtained by joining these two solutions at the inflection points of the velocity profiles. The final solution is given in terms of a series of universal functions for a fairly broad class of potential velocity distributions outside of the boundary layer. Detailed calculations of the boundary layer characteristics are worked out for the case in which the potential velocity is a linear function of the distance from the upstream stagnation point. Finally the complete separation point characteristics are determined for the boundary layer associated with a potential velocity distribution made up of two linear functions of the distance from the stagnation point. It appears that extensions of the detailed calculations to more complex potential flows can be fairly easily carried out by using the explicit formulae given in the paper.","title":"On the theory of laminar boundary layer involving separation.","url":"cran.html#doc1383"},
{"url":"cran.html#doc1289","title":"Numerical technique to lifting surface theory for calculation of unsteady aerodynamic forces due to continuous sinusoidal gusts on several wing planforms at sobsonic speeds.","description":"Murrow, H.N., pratt, K.G. And Drischler, J.A. Nasa tn.d1501, 1963. A numerical lifting-surface method has been used to calculate direct gust forces and moments on wings of several planforms. The gust velocities are continuous and vary sinusoidally in the stream direction and are also uniform across the wing span. The procedure has the advantage of rapid machine calculation and includes the effects of wing planform, nonsteady subsonic flow, and induced flow effects. The method provides for calculation of gust forces on a basis consistent with that for the calculation of forces due to motion and deformation. The results include the in-phase and quadrature components of the following quantities.. (a) spanwise distribution of section lift coefficient, (b) total lift coefficient, and (c) total pitching-moment coefficient. In addition, generalized gust forces on approximate fundamental cantilever bending modes ( parabolic) are also included. Results have been obtained for 60 and 75 delta wings, ratio 11.60, and an unswept wing of aspect ratio 6.00. Conditions for which calculations were made include two mach numbers reduced-frequency range of 0 to 1.0. The direct gust forces and moments are in forms suitable to be inserted in equations of motion used in the calculation of the dynamic responses of flexible lifting vehicles to random turbulence and to be compared with results from other methods."},
{"title":"A new series for calculation of steady laminar boundary layer flows.","url":"cran.html#doc458","description":"Gortler, H. J. Math. Mech. 6, 1957, 1. A new and general method for solving problems of plane and steady laminar boundary layer flows in incompressible fluids with arbitrary outer pressure distribution is developed. This method is based on the introduction of the dimensionless quantities as new independent spatial variables. Ordinates, u(x) the given outer velocity distribution, v the kinematic viscosity.) the solution of the boundary layer problem is then given as a power series in e with coefficient functions depending on N. This series is a formally exact solution of the boundary layer problem. The new series solution has the following qualities.. Have the significance only of cartesian coordinates, the influence of wall curvature being neglected in boundary layer theory, the new coordinates are adjusted to the data of the special problem in any case of application. The new variables represent a logical development of former efforts in the field of boundary-layer flow calculation. With other series solutions known for some special cases is that the leading term of the new series satisfies exactly the outer boundary condition at all cross-sections along the wall. Therefore, the succeeding terms give corrections only in the inner part of the boundary layer. Accordingly, taking also no. 1 into account, the zero order term by itself gives a good approximation for the boundary layer flow."},
{"url":"cran.html#doc977","title":"Concerning some solutions of the boundary layer equations in hydrodynamics.","description":"Goldstein, S. Proc. Cam. Phil. Soc. 26, 1930, 18. The boundary-layer equations for a steady two-dimensional motion are solved for any given initial velocity distribution (distribution along a normal to the boundary wall, downstream of which the motion is to be calculated). This initial velocity distribution is assumed expressible as a polynomial in the distance from the wall. Three cases are considered.. First, when in the initial distribution the velocity vanishes at the wall, but its gradient along the normal does not,. Second, when the velocity in the initial distribution does not vanish at the wall,. And Third, when both the velocity and its normal gradient vanish at the wall (as at a point where the forward flow separates from the boundary). The solution is found as a power series in some fractional power of the distance along the wall, whose coefficients are functions of the distance from the wall to be found from ordinary differential equations. Some progress is made in the numerical calculation of these coefficients, especially in the first case. The main object was to find means for a step-by-step calculation of the velocity field in a boundary layer, and it is thought that such a procedure may possibly be successful even if laborious. The same mathematical method is used to calculate the flow behind a flat plate along a stream. The results are shown in curves in the original."},
{"url":"cran.html#doc146","title":"Supersonic flow past slender bodies with discontinuous profile slope.","description":"Fraenkel and portnoy. Aero.quart. 6, 1955, 114. Ward's slender-body theory is extended to derive first approximations to the external forces on slender bodies of general cross section with discontinuous profile slope. Two classes of body are considered.. Bodies whose profile (typified by the local radius) is continuous between the nose and base, and certain bodies whose profile is discontinuous, such as bodies with annular or side air intakes and wing-bodies on which the wing has an unswept leading edge. (where air intakes are concerned, it is assumed that they are sharp-edged and that there is no /spillage/ of the internal flow). The following conclusions apply to the former class of bodies. The variation of drag with mach number is found to depend only on the discontinuities in the longitudinal rate of change of the cross-sectional area, and is thus independent of cross-sectional shape. The drag itself is unchanged if the direction of the flow is reversed. The expressions for lift and moment assume the same forms as for smooth pointed bodies, the lift depending only on conditions at the base of the body. The general theory is applied to winged bodies of revolution with an unswept wing leading edge.. The results bear a marked resemblance to those obtained by ward. The results for wings alone are seen to be applicable, with one modification, to subsonic as well as to supersonic speeds."},
{"title":"An analysis of base pressure at supersonic velocities and comparison with experiment.","url":"cran.html#doc188","description":"Chapman, dean R. Naca report 1051 In the first part of the investigation an analysis is made of base pressure in an inviscid fluid, both for two-dimensional and axially symmetric flow. It is shown that for two-dimensional flow, and also for the flow over a body of revolution with a cylindrical sting attached to the base, there are an infinite number of possible solutions satisfying all necessary boundary conditions at anh given free-stream mach numger. For the particular case of a body having no sting attached only one solution is possible in an inviscid flow, but it corresponds to zero base drag. Accordingly, it is concluded that a strictly inviscid-flow theory cannot be satisfactory for practical applications. An approximate semi-empirical analysis for base pressure in a viscous fluid is developed in a second part of the investigation. The semi-empirical analysis is based partly on inviscid-flow calculations. In this theory an attempt is made to allow for the effects of mach number, reynolds number, profile shape, and type of boundary-layer flow. Some measurements of base pressure in two-dimensional and axially symmetric flow are presented for purposes of comparison. Experimental results then are presented concerning the support interference effect of a cylindrical sting, and the interference effect of a reflected air wave on measurements of base pressure in a supersonic wind tunnel."},
{"description":"Abraham leiss National aeronautics and space administration technical note d-1507 39 by rockets exhausting upstream and downstream. An experimental investigation was made of the pressures induced on a flat plate at a free-stream mach number of 1.39 by a supersonic rocket jet exhausting upstream and downstream. Measurements of the pressure distribution on a flat plate were made at zero angle of attack for 11 different locations of the jet exhaust nozzle beneath the wing. Measurements were made at ratios of rocket-exit total pressure to free-stream static pressure from 6 to 60 and at a reynolds number per foot of approximately 10 times 10 to the power of 6. The rocket when exhausted upstream produced a strong shock that moved further upstream with increasing rocket-exit total-pressure ratio. Positive incremental normal-force coefficients were obtained at all test positions. Data at 11 test positions are tabulated for rocket-on and rocket-off pressure coefficients as well as for incremental pressure coefficients for the 48 orifices of the flat plate for the range of ratio of rocket-exit total pressure to free-stream static pressure of the investigation. Changing the location of the model with respect to the plate had a negligible effect when the rocket was varied in the chordwise direction, but the pressure coefficients were reduced as the rocket was lowered away from the flat-plate wing.","url":"cran.html#doc636","title":"Pressure distribution induced on a flat plate at a free-stream mach number of 1.39 by rockets exhausting upstream and downstream."},
{"url":"cran.html#doc707","title":"Thermal analysis of stagnation regions with emphasis on heat-sustaining nose shapes at hypersonic speeds.","description":"Hanawalt, A.J., blessing, A.H. And Schmidt, C.M. J.aero. Sc. May 1959. P. 257-263. The leading edges and noses of hypersonic vehicles are subjected to severe aerodynamic heating and must be cooled in some manner-dash E.G., internal convection, transpiration, or radiation. It is this latter mode of handling the problem that is discussed in this paper. Neglecting conduction in the leading-edge region, the maximum temperature for long-range hypersonic gliders is of the same order as the melting point of refractory materials, with a corresponding large temperature gradient away from the leading edge. Inclusion of conduction in the aft direction reduces the maximum temperature and distributes the heat to a location that will radiate it out from the surface. For either steady-state or transient conditions, the temperature at the leading edge is reduced by conduction, while the temperature aft of the leading-edge shoulder is increased, thus setting up a heat transmission balance between the convective influx of heat, the redistribution of heat by conduction, and the radiation of heat from the surface. The feasibility of such a mechanism can be enhanced by suitably choosing leading-edge shapes and materials. The philosophy behind the choice of leading-edge shapes is discussed and the effects of varying parameters, such as shape, diameter, emissivity, conductivity, thickness, etc., are shown."},
{"url":"cran.html#doc177","title":"The mixing of free axially-symmetrical jets of mach number 1.40.","description":"N. H. Johannesen Department of the mechanics of fluids, university of manchester communicated by the director-general of scientific research (air), ministry of supply 40. Axially-symmetrical, supersonic, fully-expanded jets of diameter about 0.75 in. And Of mach number 1.40 issuing into an atmosphere at rest were investigated by schlieren and shadow photography and by pressure traversing. The development of the jets was found to depend critically on the strength of the shock waves in the core of the jet at the nozzle exit. With strong shock waves present the jet spread very rapidly and was very unsteady. The jet did in some cases break up into large eddies of the same size as the diameter of the jet. When no disturbances were present in the core of the jet the spreading was far more gradual and the jet showed only slight unsteadiness. The turbulent mixing region of the first part of the jet with strong shock waves was investigated in detail by pitot tubes. The first inch was found to correspond to a two-dimensional half-jet. The velocity profiles were similar and well represented by the error integral. The rate of spreading was only half the value for low-speed flow. By integrations across the mixing region the entrainment and the loss of kinetic energy were determined. These quantities were found to agree well with the values estimated by assuming an error-integral velocity profile."},
{"description":"Glauert, M.B. And Lighthill, M.J. Proc. Roy. Soc. A, 230, 1955, 188. The laminar boundary layer in axial flow about a long thin cylinder is investigated by two methods. One (2) is a pohlhausen method, based on a velocity profile chosen to represent conditions near the surface as accurately as possible. The other (3) is an asymptotic series solution, valid far enough downstream from the nose for the boundary-layer thickness to have become large compared with the cylinder radius. Another series solution (due to seban, bond and kelly) is known, valid near enough to the nose for the boundary layer to be thin compared with the cylinder radius. The pohlhausen solution shows good agreement with both series, near and far from the nose, and enables an interpolation to be made (4) between them in the extensive range of distances from the nose for which neither is applicable. The final recommended curves, for the variation along the cylinder of skin friction, boundary-layer displacement area and momentum defect area, are displayed in graphical and tabular form (figure 1 and table 1) and are expected to be correct to within about 2. The velocity near the wall is closely proportional to the logarithm of the distance from the axis,. This is the profile used in the pohlhausen method. The analogy with the distribution of mean velocity in turbulent flow over a flat plate is discussed at the end of 2.","title":"The axisymmetric boundary layer on a long thin cylinder.","url":"cran.html#doc381"},
{"url":"cran.html#doc781","title":"Use of subsonic kernel function in an influence-coefficient method of aeroelastic analysis and some comparisons with experiment.","description":"John L. Sewall, robert W. Herr, and charles E. Watkins Technical note d-515 This paper illustrates the development and application of an influence-coefficient method of analysis for calculating the response of a flexible wing in an airstream to an oscillating disturbing force and for treating such aeroelastic instabilities as flutter and divergence. Aerodynamic coefficients are derived on the basis of lifting-surface theory for subsonic compressible flow by use of the method presented in nasa technical report r-48. Application of the analysis is made to a uniform cantilever wing-tip tank configuration for which responses to a sinusoidal disturbing force and flutter speeds were measured over a range of subsonic mach numbers and densities. Calculated responses and flutter speeds based on flexibility influence coefficients measured at nine stations are in good agreement with experiment, provided the aerodynamic load is distributed over the wing so that local centers of pressure very nearly coincide with these nine influence stations. The use of experimental values of bending and torsional structural damping coefficients in the analysis generally improved the agreement between calculated and experimental responses. Some calculations were made to study the effects of density on responses near the flutter conditions, and linear response trends were obtained over a wide range of densities."},
{"description":"Van driest, E.R. And Mccauley, W.D. J. Ae. Scs. 27, 1960, 261. Experiments were performed in the 12-in. Supersonic wind tunnel of the jet propulsion laboratory of the california institute of technology to investigate the effect of three-dimensional roughness elements (spheres) on boundary-layer transition on a tained at local mach numbers of 1.90, 2.71, and 3.67 by varying trip size, position, spacing, and reynolds number per inch. The results indicate that (1) transition from laminar to turbulent flow induced by three-dimensional roughness elements begins when the double row of spiral vortices trailing each element contaminates and breaks down the surrounding field of vorticity, (2) transition appears rather suddenly, becoming more violent with increasing roughness height relative to the boundary-layer thickness, (3) after the breakdown of the vorticity field, the strength of the spiral vortices may still persist in the sublayer of the ensuing turbulent flow, (4) lateral spacing of roughness elements has little effect upon the initial breakdown (contamination) of the laminar flow, and (5) the trip reynolds number where u and v are the velocity and kinematic viscosity at the outer edge of the boundary layer and k is roughness height, such that transition occurs at the roughness position, varies as the position reynolds number to the one-fourth power, viz., where x is trip position.","title":"The effect of controlled three-dimensional roughness on boundary layer transition at supersonic speeds.","url":"cran.html#doc7"},
{"description":"Eckhaus, W. M.I.T. Fluid dynamics res. Group R.59-3, 1959. A study is made of the unsteady flow around an airfoil at transonic mach numbers, the situation being such that local supersonic regions terminated by shock-waves are present in the vicinity of the airfoil. For the unsteady part of the flow, small perturbations technique is employed and the interaction with the shock wave is taken into account. The case of an oscillating aileron is considered first, and a solution is derived for the pressure distribution on the aileron. It is found that the solution has a simple form when the shock-wave is well ahead of the hinge axis of the aileron. As the shock approaches the hinge-axis a correction must be added to the solution. An interpretation of these results is given. The results are compared with results of a theory which neglects the presence of the shock and it is found that both agree for m = 1. For m 1, however, neglecting the presence of the shock waves introduces errors of the order of magnitude (1 - m), where m is the local mach number behind the shock. The theory is finally extended to include the case in which the whole airfoil oscillates, but only the solution for the subsonic region behind the shock is treated. The role of the unsteady shock-boundary layer interaction is discussed and it is shown that this mechanism can be included in the results of the present theory.","url":"cran.html#doc903","title":"Two dimensional transonic unsteady flow with shock waves."},
{"url":"cran.html#doc349","title":"Numerical solution of the boundary layer equations without similarity assumptions.","description":"Kramer, R.F. And Lieberstein, H. J. Ae. Scs. 26, 1959, 508. The crocco transformation combined with a mangler transformation is used to carry the boundary-layer problem for axially symmetric blunt bodies into a form suitable for direct numerical computation without introduction of similarity assumptions. Conditions which in the original problem appear at infinity now are brought to a finite straight line, and the body is transformed to a parallel line. Data can be generated on the stagnation line the equations are a parabolic system of two second-order equations, the boundary-value problem is analogous to the slab problem for the heat equation. An implicit difference equation is used to reduce stability difficulties. Special techniques in forming the difference equation result in a linear system of algebraic equations to be solved on any given line of integration, and these solutions are computed from recursion relations generated by back substitution. For bluntnosed bodies with approach flow mach numbers greater than 8 (approximately), large temperature gradients occur across a thin boundary layer of dissociated gas, and it is necessary to use real-gas effects, approximated here by certain fits to the gas tables. A case is computed, however, for a lower mach number approach flow using perfect-gas theory to provide a standard against which similarity solutions may be tested."},
{"description":"Tani, I. And Komoda, H. J. Ae. Scs.1962, 440. Results of an experimental investigation of instability leading to transition in the subsonic boundary layer flow along a flat plate are presented. A series of wings was placed outside the boundary layer to produce streamwise vortices, which in turn made the boundary layer three-dimensional--I.E., periodic in thickness in the spanwise direction. Hot-wire measurements were made to trace the downstream development of the disturbance or wave created by the vibrating ribbon. As the wave travels downstream, it is deformed into a three-dimensional configuration by the three-dimensionality of the boundary-layer flow, but it is eventually damped out so long as it remains small in intensity. It is only after the wave intensity exceeds a certain amount (which depends on the degree of boundary-layer three-dimensionality) that the nonlinear effect manifests itself by the rapid amplification of wave intensity, the rapid increase in wave three-dimensionality, and the distortion in mean velocity profile. The appearance of nonlinear development inevitably leads to the breakdown of laminar flow, and hence the onset of turbulence. There is present a mechanism by which the energy is transferred from one spanwise position to another so that the breakdown of laminar flow occurs as a consequence of three-dimensional development of the wave as a whole.","url":"cran.html#doc1220","title":"Boundary layer transition in the presence of streamwise vortices."},
{"description":"Pai, S.I. J.app.mech. 20, 1953, 109. The reynolds equations of motion of turbulent flow of incompressible fluid have been studied for turbulent flow between parallel plates. The number of these equations is finally reduced to two. One of these consists of mean velocity and correlation between transverse and longitudinal turbulent-velocity fluctuations only. The other consists of the mean pressure and transverse turbulent-velocity intensity. Some conclusions about the mean pressure distribution and turbulent fluctuations are drawn. These equations are applied to two special cases.. One is poiseuille flow in which both plates are at rest and the other is couette flow in which one plate is at rest and the other is moving with constant velocity. The mean velocity distribution and the correlation can be expressed in a form of polynomial of the co-ordinate in the direction perpendicular to the plates, with the ratio of shearing stress on the plate to that of the corresponding laminar flow of the same maximum velocity as a parameter. These expressions hold true all the way across the plates, I.E., both the turbulent region and viscous layer including the laminar sublayer. These expressions for poiseuille flow have been checked with experimental data of laufer fairly well. It also shows that the logarithmic mean velocity distribution is not a rigorous solution of reynolds equations.","title":"On turbulen flow between parallel plates.","url":"cran.html#doc257"},
{"description":"Hartunian, R.A., russo, A.L. And Marrone, P.V. J. Ae. Scs. 1960, 587. An experimental study is made of the wall boundary layer in a shock tube operated over a wide range of shock mach numbers and pressure levels in air, including those for which real-gas effects exist. Transition distances are determined and correlated in terms of the transition reynolds number based on a characteristic length for this boundary layer. Data from independent shock-tube studies are also included in this correlation. The results indicate a weak dependence of transition reynolds number on shock strength up to moderate values of shock mach number, followed by a larger stabilizing tendency. Comparison of these data with transition data obtained in the same manner in argon indicate that the increased cooling rates are largely responsible for the stabilization. A dependence of transition reynolds number on the unit reynolds number is found at the lower shock strengths. Specifically, higher transition reynolds numbers are achieved at larger unit reynolds numbers. The phenomenon of transition reversal does not appear within the range of the experiments reported. Laminar- and turbulent-flow heat-transfer rates to the walls of the shock tube are determined experimentally. The results of the heat-transfer measurements substantiate existing theories in both the laminar- and turbulent-flow regimes.","title":"Boundary layer transition and heat transfer in shock tubes.","url":"cran.html#doc1264"},
{"description":"Wittcliff, C.E. And Wilson, M.R. J. Ae. Scs. 1962, 761. As part of a general study of the aerothermodynamic characteristics of flight of hypersonic vehicles, an investigation of laminar heat transfer to slender yawed cones has been conducted. Experiments have been made in the cal 11- by 15-in. Shock tunnel at mach numbers from 11 to 13 and at yaw angles up to were tested. The heat-transfer rates are compared with theoretical predictions. The effects on the local heat-transfer rates of the boundary-layer displacement thickness, transverse curvature, yaw, nose bluntness, and the entropy sublayer are discussed. It is shown that, at zero yaw, the experimental data for the sharp cone are in good agreement with theory when boundary-layer displacement and transverse-curvature effects are included. For the yawed sharp cone, the heat-transfer rates along the most windward streamline are in good agreement with reshotko's theory for yaw angles up to 3. At larger yaw angles, the experimental heat transfer was found to be greater than that predicted theoretically. However, at these yaw angles the heat-transfer distribution on the windward side was in good agreement with laminar-boundary-layer calculations based on an assumption of local similarity. The zero-yaw tests of the blunted cones showed qualitative agreement with cheng's shock-layer theory for slender blunt-nose bodies.","url":"cran.html#doc1213","title":"Heat transfer to slender cones in hypersonic flow, including effects of yaw and nose bluntness."},
{"url":"cran.html#doc562","title":"Concerning the effect of compressibility on laminar boundary layers and their separation.","description":"Howarth, L. Proc. Roy. Soc. A, 194, 1948. The theory of compressible flow in a laminar boundary layer has been developed for the case when the viscosity is assumed to be proportional to the absolute temperature and the prandtl number is unity. (these assumptions may be compared with the empirical relations suggested by cope.) it is shown that a transformation of the ordinate normal to the layer can lead to a simplified form of equation of motion very similar to the ordinary incompressible equation but modified by a multiplicative factor g in the pressure term. This factor is greater than unity at the boundary and tends to one at the outside of the layer. Several particular solutions are considered including accelerated flow with a linearly increasing velocity and retarded flow along a flat plate with a linearly decreasing velocity. The general implications of the theory are discussed and qualitative conclusions are drawn when the mainstream velocity starts from a stagnation point, rises to a maximum and subsequently falls. It is concluded that for such a velocity distribution increasing compressibility will reduce the skin friction, increase the boundary layer thickness and cause earlier separation as compared with the incompressible flow with the same mainstream velocity distribution and the kinematic viscosity corresponding to conditions at the stagnation point."},
{"description":"Cheng, H.K. J. Fluid mech. 12, 1962, 169. A detailed treatment of inviscid hypersonic flow past a circular cone is given, for small and moderate yaw angles, within the framework of shock-layer theory. The basic problem of non-uniform validity associated with the singularity of the entropy field is examined and a valid first-order solution is obtained which provides an explicit description of a thin vortical layer at the inner edge of the shock layer. Analytic formulas for pressure and circumferential velocity are given consistent to the second-order approximation including the non-linear yaw effect. The study of the entropy field (which is not restricted to the hypersonic case) also provides corrections to previous work on the yawed cone and confirms the validity of the linear yaw effect on pressure field in the stone theory. A related investigation of three-dimensional flow fields is presented with special reference to the flow structure near the surface of a pointed, but otherwise arbitrary body. The inviscid streamline pattern on the surface is given by the geodesics originting from the pointed nose as a leading approximation of shock-layer theory. Associated with this streamline pattern is a vortical sublayer which exists generally at small as well as at large angle of attack. At the base of the sublayer, enthalpy and flow speed remain essentially uniform.","title":"Hypersonic flows past a yawed circular cone and other pointed bodies.","url":"cran.html#doc1309"},
{"url":"cran.html#doc1184","title":"Three dimensional effects in viscous wakes.","description":"Steiger, M.H. And Bloom, M.H. Aiaa jnl. 1963, 776 Three-dimensionality in wakelike or jetlike free mixing may stem from initial geometric configurations, nonuniformities in flow variables over a cross section, or boundary conditions along the flow. These may be generated by bodies at angle of attack, nonaxisymmetric bodies, mixing of nonaxisymmetric jets with an outer flow, finite wings, or more artificial means. This paper is devoted to studies bearing on such configurations. The first section deals with the general mathematical model, in which the boundary layer approximations are used, and with methods of solution. Laminar and turbulent flow, compressibility, unsteadiness, and streamwise pressure gradients are admitted initially. The flux forms of the equations are given. Algebraic integrals of the energy equations and the diffusion ( frozen-flow) equations are obtained. A simplification of the convective terms, roughly corresponding to the oseen approximation, is used in the asymptotic downstream region. The second section contains explicit solutions for specific configurations, in particular for flows whose initial isovels are of elliptic shape. These flows may be wakelike or jetlike. Compressibility is admitted,. However, the flows must have uniform pressure and must be steady. The final section deals with interpretation and evaluation of the results."},
{"description":"Vaglio-laurin, R. J. Ae. Scs. 1960, 27. Recent results obtained for three-dimensional laminar boundary layers are extended to the turbulent case. It is shown that in the presence of highly cooled surfaces and of moderate mach numbers of the outer stream, the crossflow and the pertaining reynolds stresses in a general three-dimensional turbulent boundary layer are negligible even for large transverse pressure gradients. A correlation due to mager between two- dimensional compressible and incompressible turbulent boundary layers is extended to the problem in question. From a study of the transformation and of its implications, a rapid method for the analysis of the boundary-layer flow under the subject conditions is established. In the absence of general three- dimensional data, a comparison with experiments and with the predictions of other known analyses is carried out for several axisymmetric configurations,. The results of the method presented here exhibit good agreement with the data. The range of validity of the cold wall approximation for general three-dimensional problems is estimated qualitatively on the basis of recent measurements in laminar flow, the argument being that, for either zero or favorable streamwise pressure gradients, smaller three-dimensional effects are to be expected in a turbulent boundary layer, as compared to a laminar layer.","url":"cran.html#doc1281","title":"Turbulent heat transfer on blunt-nosed bodies in two-dimensional and general three-dimensional hypersonic flow."},
{"url":"cran.html#doc815","title":"Investigation of several blunt bodies to determine trans- onic aerodynamic characteristics including effects of spinning and of extendible afterbody flaps and some measurements of unsteady base pressures.","description":"Fisher, L.R. And Dicamillo, J.R. Nasa memo 1-21-59l, 1959. Several blunt bodies having shapes that may be suitable for atmospheric reentry vehicles were tested to determine the aerodynamic characteristics of such shapes for angles of attack up to 34. The tests were conducted through the transonic mach number range and at reynolds numbers from 1.74 x 10 to 2.78 x 10, based on body diameter. A full-skirted rather than a short-skirted type of shape developed the greatest amount of static stability and the largest lift-curve slopes. The angle of attack for maximum lift for such bodies appears to be subject to mach number effects. Spinning a full-skirted body about its longitudinal axis generally increased the lift and reduced the pitching moment at angles of attack and reduced the aerodynamic static stability parameter through the transonic mach number range. The extension of segmented clamshell-shaped flaps from the afterbody of a short-skirted model served to increase the lift and static stability only if the flaps extended into the airstream. Some evidence was found of oscillatory base pressures on two dissimilar shapes at certain high angles of attack and the highest mach number in these tests. There is doubt, however, that these pressures can induce any significant oscillatory motion for a reentry vehicle because of their small amplitude and phasing."},
{"url":"cran.html#doc53","title":"Transition reynolds numbers of separated flows at supersonic speeds.","description":"Larson, H.K. And Keating, S.J. Nasa tn.d349, 1960. Experimental research has been conducted on the effects of wall cooling, mach number, and unit reynolds number on the transition reynolds number of cylindrical separated boundary layers on an ogive-cylinder model. Results were obtained from pressure and temperature measurements and shadowgraph observations. The maximum scope of measurements encompassed mach numbers between 2.06 and 4.24, reynolds numbers (based on length of separation) between 60, 000 and 400, 000, and ratios of wall temperature to adiabatic wall temperature between 0.35 and 1.0. Within the range of the present tests, the transition reynolds number was observed to decrease with increasing wall cooling, increase with increasing mach number, and increase with increasing unit reynolds number. The wall-cooling effect was found to be four times as great when the attached boundary layer upstream of separation was cooled in conjunction with cooling of the separated boundary layer as when only the separated boundary layer was cooled. Wall cooling of both the attached and separated flow regions also caused, in some cases, reattachment in the otherwise separated region. Cavity resonance present in the separated region for some model configurations was accompanied by a large decrease in transition reynolds number at the lower test mach numbers."},
{"url":"cran.html#doc1051","title":"The stability of thin-walled unstiffened circular cylinders under axial compression including the effects of internal pressure.","description":"Harris, L.A. J. Ae. Scs. 24, 1957, 587. In the design of high-speed aircraft the importance of unpressurized and pressurized monocoque cylinders necessitates a reliable analysis procedure for the compressive buckling of cylindrical shells. Analysis by the classical small-deflection theory has proved inadequate. Recent large-deflection theoretical treatments of the problem have shown reasonable correlation with experiments but require a prior knowledge of the initial imperfections of the cylinder. Developed in this paper is a semiempirical procedure which permits a compressive buckling analysis of cylindrical shells with a knowledge of the cylinder geometry only. This analysis is achieved by correlating experimental data statistically with theoretical parameters. In order to provide data not previously available, an extensive series of axial compression tests of pressurized cylinders has been performed. These data, together with all other known test data, are analyzed semiempirically. In the analysis best-fit curves are presented using theoretical parameters and shapes of curves where applicable. Unpressurized and pressurized cylinder compressive buckling curves are then developed as 90 per cent probability curves from the test data. In general, these statistically defined design curves are significantly lower than previously available design curves."},
{"description":"Spahr, J.R. Naca tn.4146, 1958. A wind-tunnel investigation was conducted at a mach number of 1.96 and at reynolds numbers (based on the mean aerodynamic chord of the exposed wing) of 0.36 and 1.03 million to determine the normal forces, pitching moments, and rolling moments contributed by each wing panel of a cruciform-wing and body combination over a wide range of combined angles of pitch and roll. The wings were triangular of aspect ratio 2, and the body was an ogive-cylinder combination. The effects of forebody length and roughness and of the presence of the adjacent panels on these panel contributions were determined. The results of the investigation show that large changes in the panel forces and moments can occur as the result of combined angles. A general theoretical method based on slender-body and strip theories was found to yield results in good agreement with the wind-tunnel measurements. These comparisons indicate that the changes in the panel characteristics due to combined angles are caused primarily by a cross coupling between the side-wash velocities due to angle of attack and sideslip and by the presence of forebody vortices due to crossflow separation. It was found that an increase in forebody length increases the effect of the forebody vortices because of the dependence of the strength of these vortices on the forebody length.","url":"cran.html#doc434","title":"Contributions of the wing panels to the forces and moments of supersonic wing-body combinations at combined angles."},
{"description":"Samson, S.H. And Bergmann, H.W. J. Ae. Scs. 27, 1960, 679. Two methods are presented for the analysis of complex low- aspect-ratio aircraft structures. Both methods provide for arbitrary external loading, are general with respect to the orientation of structural members, and permit arbitrary boundary conditions. For purposes of analysis a structure is idealized as a network of flexural members with interconnected torsion boxes. In the first method, sets of linear equations are obtained by expressing boundary conditions, member deflection equations, equilibrium requirements, and slope-compatibility relationships in terms of deflections and internal forces. The solution for deflections and internal forces is then formed as the product of an inverse structural matrix and a column matrix of load functions. In the second method, the conditions at a given boundary are assembled as a column matrix and are transferred in a step by-step fashion over the entire structure to an opposite boundary. The transfer is accomplished by successive multiplications of square matrices composed independently for the different transfer ranges. The final operation is the inversion of a relatively small matrix and provides the solution for the unknown boundary conditions. Comparisons of theoretical results with experimental data and electric-analog solutions are favorable.","title":"Analysis of low-aspect-ratio aircraft structures.","url":"cran.html#doc47"},
{"title":"The equilibrium piston technique for gun tunnel operation.","url":"cran.html#doc595","description":"East, R.A. And Pennelegion, L. Arc 22, 852, 1961. A modified technique for the operation of a gun tunnel is suggested based on experimental results. If the piston mass and the initial barrel pressure are chosen correctly, then the peak pressures associated with the gun tunnel may be eliminated. Under these conditions the piston is brought to rest with no overswing. Some measurements of the piston motion using a microwave technique are reported which confirm this idea. The wave diagram associated with this mode of operation is shown, and some calculations of the stagnation pressure are given which show that during the suggested running time, the stagnation pressure may be considerably greater than the driving pressure if the driving chamber cross-sectional area is large compared with that of the driven section. For a uniform shock tube the stagnation pressure will always be less than the driving pressure. The use of air, helium and hydrogen as driving gases has been considered. Experiments in a gun tunnel are reported which show that the equilibrium piston technique enables steady stagnation pressures to be achieved over a time of approximately 15 ms using air as the driving gas. The expansion caused by the piston acceleration is shown to interact with the stationary piston, but this is found to produce only a small drop in stagnation pressure."},
{"url":"cran.html#doc1386","title":"Analysis and calculation by integral methods of laminar compressible boundary layer with heat transfer and with and without pressure gradient.","description":"Morduchow, M. Naca R.1245, 1955. A survey of integral methods in laminar-boundary-layer analysis is first given. A simple and sufficiently accurate method for practical purposes of calculating the properties layer in an axial pressure gradient with heat transfer at the wall is then presented. For flow over a flat plate, the method is applicable for an arbitrarily prescribed distribution of temperature along the surface and for any given constant prandtl number close to unity. For flow in a pressure gradient, the method is based on a prandtl number of unity and a uniform wall temperature. A simple and accurate method of determining the separation point in a compressible flow with an adverse pressure gradient over a surface at a given uniform wall temperature is developed. The analysis is based on an extension of the karman-pohlhausen method to the momentum and thermal energy equations in conjunction with fourth- and especially higher degree velocity and stagnation-enthalpy profiles. From the equations derived here, conclusions regarding the effect of pressure gradient, mach number, and wall temperature on the boundary-layer characteristics are derived and illustrated. In particular the effects on skin-friction, heat-transfer coefficient, separation point in an adverse pressure gradient, and stability of the laminar boundary layer are analyzed."},
{"description":"Schmidt, R. And Wempner, G.A. Asme trans. 81e, 1959, 681. The large symmetric deformations of shallow conical shells are of interest in the design of nonlinear conical disk springs. In most applications a uniformly distributed axial load acts at the inner and outer edges,. These edges are otherwise free. Several approximations have been proposed to describe the behavior of these springs. A first approximation (1) is based on the assumption that meridional strains are negligible. This requires that the shell remain conical after deformation and also that the extensional strain of meridional lines on the middle surface vanish. Another approximation (2) retains only the assumption that the shell remains conical. The first assumption satisfies neither of the two boundary conditions at the free edges,. The latter violates the condition of vanishing moment at the free edges. Recently the authors presented a series solution (3) for a special case, namely, the case of an annular plate under similar loading. Numerical solutions for the shallow conical shell under these conditions of load have also been obtained (4). An examination of these results indicates that the meridional bending stresses are of much smaller magnitude than the circumferential bending stresses. Hence the present analysis is based on the neglect of the meridional bending moment.","title":"The nonlinear conical spring.","url":"cran.html#doc1059"},
{"description":"Beckwith, I.E. Naca tn.4345, 1958. Heat-transfer and skin-friction parameters obtained from exact numerical solutions to the laminar compressible-boundary-layer equations for the infinite cylinder in yaw are presented. The chordwise flow in the transformed plane is of the falkner-skan type. Solutions are given for chordwise stagnation flow with both a porous and a nonporous wall. The effect of a linear viscosity-temperature relation is compared with the effect of the sutherland viscosity-temperature relation at the stagnation line of the cylinder for a prandtl number of 0.7. The effects of pressure gradient, mach number, yaw angle, and wall temperature are investigated for a linear viscosity-temperature relation and a prandtl number of 1.0 with a nonporous wall. The results indicate that compressibility effects become important at large mach numbers and yaw angles, with larger percentage effects on the skin friction than on the heat transfer. The use of the two different viscosity relations gives about the same results except when large changes in temperature occur across the boundary layer, as for a highly cooled wall. The present solutions predict that a larger amount of coolant would be required at a given large mach number and yaw angle than would be predicted from solutions of the corresponding incompressible-boundary-layer equations.","title":"Similar solutions for the compressible boundary layer on a yawed cylinder with transpiration cooling.","url":"cran.html#doc565"},
{"description":"Reissner, E. J. Math. Phys. 25, 1946, 80. The purpose of the present paper is to derive a system of equations which can be used for the analysis of shallow segments of thin, elastic, spherical shells. A segment will be called shallow if the ratio of its height to base diameter is less than, say. The results obtained on the basis of this assumption will often also be applicable to shells which are not shallow, namely then, when the loads are such that the stresses are effectively restricted to shallow zones. The problem of the spherical elastic shell has been the subject of numerous researches. For the rotationally symmetric case the fundamental results were obtained in 1912 (1) and have been the starting point of many applications. While it is possible to deduce from these results approximate equations equivalent to part of what follows, it is believed that the present approach to the problem of the shallow shell may be of some interest even for rotationally symmetric cases. A number of investigations have been concerned with the shell loaded in a non-rotationally symmetric manner (2, 3, 4). In its general form this problem is quite difficult and the results so far obtained are not easy to apply. Restricting attention to the shallow shell in the manner of the present paper brings with it a very considerable simplification of the analysis.","url":"cran.html#doc828","title":"Stresses and small displacements of shallow spherical shells."},
{"title":"The analytical design of an axially symmetric laval nozzle for a parallel and uniform jet.","url":"cran.html#doc341","description":"Foelsch, K. J. Ae. Scs. 16, 1949. The equations for the nozzle's contours are derived by integration of the characteristic equations of the axially symmetric flow. Since it is not possible to integrate these equations mathematically in an exact form, it was necessary to find a way to approximate the calculations. The approximation offers itself by considering and comparing the conditions of the flow in a cone with those in a nozzle, as a linearization of the characteristic equations. The first part of the report deals with equations for the transition curve by which the conical source flow is converted into a parallel stream of uniform velocity. The equations are derived by integration along a mach line of the flow in the region where the conversion takes place. A factor f is introduced expressing a relation between the direction and the velocity of the flow along a certain mach line. F remains undetermined and is not involved in the final equations. In the second part of the report, the spherical sonic flow section is converted into a plane circular section of the throat. The nozzle's contour adjacent to the throat is formed by the arc of a circle connected with the transition curve by a straight line. The gas dynamic properties of the boundary mach line are calculated in table 1, the use of which shortens the calculations considerably."},
{"url":"cran.html#doc907","title":"Cavitation and pressure distribution head forms at zero angle of yaw.","description":"Hunter rouse and john S. Mcnown Iowa institute of hydraulic research, state university of iowa iowa city Early in the fall of 1943 the iowa institute of hydraulic research undertook the design and fabrication of a variable-pressure water tunnel. As the tunnel neared completion, however, its immediate use for the study of the pressure distribution around various body forms was requested. The original request for this investigation was a natural out-growth of the need for systematic data on the distribution of pressure in flow around various bodies, particularly under conditions leading to cavitation, information which is desirable for the design of a wide variety of navy equipment. Ultimately the study is to include data for two- and three-dimensional head and tail forms at various angles of yaw. The first phase of the study, namely the investigation of three-dimensional head forms at zero angle of yaw, is described herein. Three general geometric series have been studied.dash rounded, ellipsoidal, and conical.dash together with other related forms. The data obtained have been systematized to yield information for a wide variety of geometrical forms either directly or by interpolation. Whenever possible, analytical methods have been used to corroborate the experimental data and to provide a reliable means of generalizing the results."},
{"description":"This paper considers the implications of recent advances in knowledge of the behaviour of boundary layers in supersonic flow. Only the simplest case is considered-dashthat of the two-dimensional boundary layer on a flat plate, with nominal zero longitudinal pressure and temperature gradients. It is shown that the empirical/intermediate enthalpy/used with success in approximations for skin friction, etc., of laminar boundary layers is closely the same as the mean enthalpy with respect to velocity. Furthermore, the mean enthalpics of laminar and turbulent boundary layers may be the same. A nonrigorous approach is made to the problems of self-induced pressure gradients, and the indications are that their effects on laminar skin friction, etc., may become noticeable at mach numbers greater than 5 and they increase as the surface temperature builds up towards zero heat-transfer conditions. The effects with turbulent boundary layers may not be so severe. Finally, the results are applied to give an idea of the magnitude of the drag and aerodynamic heating problems up to m 10, and one result is that, if there is any conflict at the higher mach numbers between surface conditions required for high radiative emissivity and those which may be thought necessary for preserving a laminar boundary layer, then it may be better to choose the former.","url":"cran.html#doc406","title":"On the behaviour of boundary layers at supersonic speeds."},
{"url":"cran.html#doc542","title":"Biot's variational principle in heat conduction.","description":"Lardner, T.J. A.I.A.A. J. 1963, 196. Biot's variational principle is applied to a number of different one-dimensional heat conduction problems. These problems show the applicability of the variational principle to problems involving prescribed heat flux boundary conditions and to those with temperature-dependent material properties. A method is introduced for including boundary conditions when these are expressed as prescribed heat fluxes. The idea behind this is overall energy balance within the body, which is a constraint condition to be satisfied by the time histories of the generalized coordinates. The variational principle is then applied to the well-known problem of constant surface heat flux in order to present the technique and provide a basis for the remaining sections. The equivalence of the result obtained in applying the variational principle for a prescribed surface temperature history to that obtained for a prescribed heat flux is also pointed out. Radiation cooling due to fourth power radiation from semi-infinite solids and finite slabs together with radiation according to newton's law of cooling is then treated. Finally, the introduction of temperature-dependent material properties is discussed and the determination of the temperature distribution in a semi-infinite solid with variable properties is investigated."},
{"description":"Deich, M.E. Naca tm.1393, 1956. Paper is a translation of chap. 7 of the book /technical gas-dynamics/ (see amr 9, rev 1869). The topics treated are best shown by the list of paragraph headings. They are.. 7-1. Geometrical and gasdynamical parameters of the lattices,. Fundamentals of flow through lattices,. 7-2. Theoretical methods of investigation or plane potential flow of incompressible fluid through a lattice,. 7-3. Electro-hydrodynamic analogy,. 7-4. Forces acting on an airfoil in a lattice,. Theorem of joukowsky for lattices,. 7-5. Fundamental characteristics of lattices,. 7-6. Friction losses in plane lattice at subsonic velocities,. 7-7. Edge losses in plane lattice at subsonic velocities,. 7-8. Several results of experimental investigations of plane lattices at small subsonic velocities,. 7-9. Flow of gas through lattice at large subsonic velocities,. Critical mach number for lattice,. 7-10. Profile losses in lattices at large subsonic velocities,. 7-11. Flow of a gas through reaction lattices at supersonic pressure drops,. 7-12. Impulse lattices in supersonic flow,. 7-13. Losses in lattices at near sonic and supersonic velocities,. 7-14. Computation of angle of deflection of flow in overhang section of a reaction lattice at supersonic pressure drops,. 7-15. Characteristic features of three-dimensional flow in lattices.","title":"Flow of gas through turbine lattices.","url":"cran.html#doc427"},
{"description":"Varley, E. J. Fluid mech. Vol. 3. 1958, P. 601-614. An estimate is given of the distribution of skin frictional force per unit length, and of displacement area, on the outside of a semi-infinite cylinder, of arbitrary cross-section, moving steadily in a direction parallel to its generators. A pohlhausen method is employed with a velocity distribution chosen to yield zero viscous retarding force on the boundary layer approximations. /the smallness of the fluid acceleration far from the leading edge has been pointed out by batchelor reasonable results atlarge distances from the leading edge. However, for a large class of cross-sections, which includes all convex cross-sections and locally concave cross-sections with re-entrant angles greater than 1/2, the method yields the expected square root growth of the boundary layer at the leading-edge, with a fairly close approximation to the coefficient, and it is supposed that the skin-frictional force and displacement area are given with reasonable accuracy along the whole length of the cylinder. Results for the elliptic cylinder and the finite flat plate are given in closed form, valid for the whole length of the cylinder, and are expected to be in error by at most 20 per cent. In addition, some estimate is given of the effect of corners on skin frictional force and displacement area.","title":"An approximate boundary layer theory for semi-infinite cylinders of arbitrary cross-section.","url":"cran.html#doc788"},
{"description":"Arnold, R.N. And Warburton, G.B. Proc. Roy. Soc. A, 197, 1949, 238. The paper deals with the general equations for the vibration of thin cylinders and a theoretical and experimental investigation is made of the type of vibration usually associated with bells. The cylinders are supported in such a manner that the ends remain circular without directional restraint being imposed. It is found that the complexity of the mode of vibration bears little relation to the natural frequency,. For example, cylinders of very small thickness-diameter ratio, with length about equal to or less than the diameter, may have many of their higher frequencies associated with the simpler modes of vibration. The frequency equation which is derived by the energy method is based on strain relations given by timoshenko. In this approach, displacement equations are evolved which are comparable to those of love and flugge, though differences are evident due to the strain expressions used by each author. Results are given for cylinders of various lengths, each with the same thickness-diameter ratio, and also for a very thin cylinder in which the simpler modes of vibration occur in the higher frequency range. It is shown that there are three possible natural frequencies for a particular nodal pattern, two of these normally occurring beyond the aural range.","title":"Flexural vibrations of the walls of thin cylindrical shells having freely supported ends.","url":"cran.html#doc844"},
{"title":"An experimental investigation of the interaction between shock waves and boundary layers.","url":"cran.html#doc1364","description":"Gadd, G.E., holder, D.W. And Regan, J.D. Proc. Of the roy. Soc. Of london, ser. A., vol. 226, 1954, pp. 227-253 An account is given of an investigation into the interaction between the boundary layer on a flat plate and a shock wave produced either externally, by a wedge in the supersonic mainstream, or from within the boundary layer, by a wedge held in contact with the plate. A wide range of free-stream mach numbers, boundary-layer reynolds numbers, and shock strengths has been covered, shock strength being defined as the ratio of the static pressure downstream of the shock to the static pressure upstream of it. Variations in these parameters can have large effects on the interaction, and there are also large differences between cases with externally generated shocks and cases where the shock is generated from within the boundary layer. The investigation has thrown light on the physical mechanisms involved. It is found that many of the major features of the interaction arise because the boundary layer separates from the surface ahead of the shock wave. The conditions under which separation occurs and the behaviour of the separated boundary layer thus have important effects, in terms of which, for example, the differences between the interactions observed with laminar and with turbulent boundary layers may be explained."},
{"description":"Morris, D.N. J.aero.scs. 28, 1961, 563. A number of approximate theories for supersonic and hypersonic flow over bodies of revolution at zero angle of attack are appraised by a critical comparison with characteristics and second-order results, with the use of hypersonic similarity as a basis for the comparison. Most of the approximate theories are inadequate except over very limited ranges of fineness ratio and mach number. The combination of second-order supersonic theory and second-order shock-expansion theory provides consistently good results throughout the supersonic speed range. On the basis of exact (or nearly exact) supersonic solutions and a limited amount of test data and theory in the transonic region, summary design curves are developed that give the pressure drag of conical and ogive noses and conical and ogive boattails over the complete range of transonic, supersonic, and hypersonic mach numbers. Other shapes can be analyzed in the same manner, provided that an equivalent amount of data is available. The analysis is made with the assumption of inviscid flow, so that the effects of boundary-layer growth, shock boundary-layer interaction, and flow separation are not included. The present correlations provide a sound basis of inviscid-flow results from which these additional viscous effects can be evaluated.","url":"cran.html#doc124","title":"A summary of the supersonic pressure drag of bodies of revolution."},
{"description":"Part ii. With oblate atmosphere. King-hele, D.G., cook, G.E. And Walker, D.M.C. R.A.E. Tn. Gw. 565. 1960. Part ii. With oblate atmosphere. The effect of air drag on satellite orbits of small eccentricity e/0.2/ was studied in part i/technical note no.G.W.533/on the assumption that the atmosphere was spherically symmetrical. Here the theory is extended to an atmosphere in which the surfaces of constant density are spheroids of arbitrary small ellipticity. Equations are derived which show how perigee distance and orbital period vary with eccentricity, and how eccentricity is related to time. Expressions are also obtained which give lifetime and air density at perigee in terms of the rate of change of period. In most of the equations, terms of order e and higher are neglected. The results take different forms according as the eccentricity is greater or less than about 0.025, while circular orbits are dealt with in a separate section. The results are also presented graphically in a manner designed for practical application, and examples of the theory in use are given. The influence of atmospheric oblateness is difficult to summarize fairly simultaneously assume their'worst'values, some of the spherical-atmosphere results can be altered by up to 30( as a result of oblateness and 5-10( would be a more representative figure.","title":"The contraction of satellite orbits under the influence of air drag.","url":"cran.html#doc614"},
{"description":"Morduchow, M. And Clarke, J.H. Naca tn.2784, 1952. The karman-pohlhausen method is extended primarily to sixth-degree velocity profiles for determining the characteristics of the compressible laminar boundary layer over an adiabatic wall in the presence of an axial pressure gradient. It is assumed that the prandtl number is unity and that the coefficient of viscosity varies linearly with the temperature. A general approximate solution which permits a rapid determination of the boundary-layer characteristics for any given free-stream mach number and given velocity distribution at the outer edge of the boundary layer is obtained. Numerical examples indicate that this solution will in practice lead to results of satisfactory accuracy, including the critical reynolds number for stability. For the special purpose of calculating the location of the separation point in an adverse pressure gradient, a short and simple method, based on the use of a seventh-degree velocity profile, is derived. The numerical example given here indicates that this method should in practice lead to sufficiently accurate results. For the special case of flow near a forward stagnation point it is shown that the karman-pohlhausen method with the usual fourth-degree profiles leads to results of adequate accuracy, even for the critical reynolds number.","title":"Method for calculation of compressible laminar boundary layer characteristics in axial pressure gradient with zero heat transfer.","url":"cran.html#doc54"},
{"description":"Dragutin stojanovic University of beograd, jugoslavia Conditions for the existence of similar solutions are known for (a) two-dimensional, incompressible, steady and nonsteady laminar boundary layers and (b) three-dimensional, incompressible, steady, laminar boundary layers for a body of revolution rotating in a fluid at rest or a body of revolution in a rotating fluid flow. Corresponding conditions for the existence of similar temperature boundary layers in both cases are given for constant and variable wall temperatures. The general conclusion is that, in all these cases, with or without viscous heating, and with constant wall temperature, conditions for the existence of similar velocity boundary layers are at the same time the conditions for the existence of similar temperature boundary layers. If the wall temperature is variable, the conditions for the existence of similar velocity boundary layers are at the same time the conditions for the existence of similar temperature boundary layers if the wall temperature varies as a power of the local free-stream velocity or surface velocity. Numberical solutions are given for the nondimensional temprature distributions function and the nondimensional temperature gradient at the wall for several prandtl numbers in the case of a rotating flow over an infinite plate at rest.","title":"Similar temperature boundary layers.","url":"cran.html#doc1149"},
{"url":"cran.html#doc601","title":"Calculation of the flow past slender delta wings with leading edge separation.","description":"Mangler, K.W. And Smith, J. Rae R. Aero.2593, 1957. The flow past a slender delta wing with a sharp leading edge, at incidence, usually separates along this edge, I.E. A vortex layer extends from the edge and rolls up to form a /core/ (a region of high vorticity). A potential flow model of this is constructed in which the layer is replaced by a vortex sheet which is rolled up into a spiral in the region of the /core/. This problem is reduced to a two-dimensional one by assuming a conical field and using slender wing theory. The shape and strength of the sheet are determined by the two conditions that it is a stream surface and sustains no pressure difference. Use is made of results previously obtained for the core region and the remaining finite part of the sheet is dealt with by choosing certain functions for its shape and strength. The parameters in these functions are found by satisfying the two conditions stated above at isolated points. Results are obtained for the pressure distribution, chord loading and norman force coefficient as functions of the ratio of the incidence to the apex angle. The lift for a given incidence is about 15 below that found by brown and michael. Flow patterns are indicated in two typical cases. The effect of separation on the drag due to lift of a wing with small thickness is discussed."},
{"description":"Mcgregor, I. The vapour screen method of flow visualisation in supersonic wind tunnels is outlined, and the development of a suitable technique for use in the 3 ft tunnel described, together with the associated optical and photographic equipment. The results of tests to determine the humidity required to produce an optimum density of fog in the working section over the mach number range temperature discussed. Numerous vapour screen photographs of the flow over and behind delta wings are included and some comparisons made with the corresponding surface oil-flow patterns. The process of condensation, the physical and optical properties of the resulting fog, and the formation of the vapour screen picture are all considered in some detail. The effects of humidity on the mach number and static pressure in the working section were investigated and the results are compared with theoretical estimates at a nominal mach number of 2.0. It is shown that the adverse effects of condensation on the flow at high mach numbers may be alleviated by the use of liquids with a lower latent heat of evaporation than water, and some results obtained at a mach number of the possibility of extending the vapour screen technique to transonic and subsonic speeds is also considered, and some results obtained at a mach number of 0.85 are included.","title":"Development of the vapour screen method of flow visualization in the 3ft tunnel at rae bedford.","url":"cran.html#doc466"},
{"title":"Longitudinal aerodynamic characteristics at low subsonic speeds of a highly swept wing utilizing nose deflection for control.","url":"cran.html#doc638","description":"Spencer, B. Nasa tn.d1482, 1962. An investigation has been conducted in the langley 7- by 10-foot transonic tunnel at low subsonic speeds to determine the longitudinal aerodynamic characteristics associated with deflection of the nose section of a highly swept delta wing having an aspect ratio of 1.33. In order to illustrate the effectiveness of this forward control, the longitudinal control characteristics are also presented for the wing with upper-and lower-surface split flaps located at the trailing edge. Comparison between the longitudinal aerodynamic characteristics of the wing utilizing the nose control and those of the wing utilizing the upper-surface split flap located at the trailing edge indicated similar control effectiveness for high control deflections (15) and similar values of trimmed lift-drag ratio with increasing lift coefficient. Use of the nose control, however, indicated a lower value of trimmed angle of attack for a given value of trimmed lift coefficient than that realized from use of the upper-surface split flap. Further reductions in trimmed angle of attack for a given value of trimmed lift coefficient may be realized from deflection of the lower-surface split flap at the wing trailing edge in combination with the nose control and would be accompanied by large reductions in lift-drag ratio."},
{"description":"Robert L. Kosson Grumman aircraft engineering corporation, bethpage, N.Y. This paper presents an approximate solution for two-dimensional, incompressible, laminar boundary layer flow with arbitrary pressure gradient. Von mises' form of the boundary layer equation is linearized by making a change in the coefficient of one of the terms. The linearized equation yields a solution that is accurate for the outer portion of the flow but inaccurate near the surface. A separate inner solution then is developed which is accurate at the surface and which joins with the outer solution at some point within the boundary layer. The method may be considered a major modification of one developed earlier by von karman and millikan, with changes in both outer and inner solutions, and the point at which the two solutions are joined. The changes improve the accuracy of the method and in some respects simplify the calculations. As examples, results are presented for flow with a linear variation of velocity (including flat plate and stagnation point flow as special cases), flow with sinusoidal variation of velocity, flow past a circular cylinder (heimenz' velocity distribution), and flow past an ellipse (schubauer's data). Agreement with theoretically exact solutions is good, and better than results obtained using the pohlhausen method.","title":"An approximate solution for laminar boundary layer flow.","url":"cran.html#doc1182"},
{"description":"Chrichlow, W.J. And Haggenmacher, G.W. J. Ae. Scs. 27, 1960, 595. Large-scale redundant structure analyses are currently feasible by the use of modern high-speed digital computers. This capability opportunely meets the urgent need to solve complex problems which otherwise would be hopelessly beyond the capacity of the hand desk computer. However, the difficulties have now shifted from tedious hand computations to the problems of adequately representing the structure by a model and of the peculiarities of irregular geometrical configurations. A wide scope of problem types can be handled by a generalized program approach. Matrix formulation is used for the organization of input data and for handling data transfer in the large complex of subroutines, including the formation of equilibrium and continuity conditions to the final loads and deflections. Simultaneous treatment of thermal expansions and plasticity is included. The use of minimum-size redundant systems is emphasized, starting from the philosophy of cutting members to provide a statically determinate structure. Improved numerical accuracy and problem size capacity is gained for a given computer. Examples are discussed ranging from simple plane-load diffusion problems to pressurized fuselage cutouts and complex wing-fuselage-shell intersection-type problems.","url":"cran.html#doc92","title":"The analysis of redundant structures by the use of high-speed digital computers."},
{"title":"The influence of two-dimensional stream shear on airfoil maximum lift.","url":"cran.html#doc453","description":"The cornell aeronautical laboratory is conducting a program of theoretical and experimental research on low-speed aerodynamics as applied to stol and vtol aircraft. The objective of this program is to re-examine certain aspects of classical aerodynamic information, in the light of low-speed flight requirements, with the aim of seeking aerodynamic processes which might be exploited to enhance law-speed performance. One aspect of propeller-driven aircraft which has recently received increasing attention is the existence of strong gradients of longitudinal velocity, or shear, in the propeller slipstream. This slipstream shear interacts with a wing surface and can alter the wing characteristics. In theoretical treatments of a wing interacting with a propeller slipstream, the first important simplification is the replacement of the slipstream with an ideal uniform jet, free of all velocity gradients. The application of these theories requires that one equate the actual slipstream to an effective uniform jet. One method employed is to assume the uniform jet has a momentum flux equal to the average in the propeller slipstream. These and similar procedures are well founded on momentum considerations., however, the implicit assumption is that the flow nonuniformity, the shear, does not influence the wing characteristics."},
{"description":"Smith, G.E. Rae R. Struct.269, 1961. The critical flutter speed is evaluated for a two-dimensional thin buckled panel with one surface exposed to a supersonic airstream and the other to still air at the same static pressure. The panel is simply supported along the leading and trailing edges by rigid edge members separated by an elastic member represented by a compression spring. The whole system is acted upon by a constant compressive force uniformly distributed along the edge members. The aerodynamic forces acting on the deflected panel are found from two-dimensional /quasi-steady/ theory, valid for slow oscillations where the downwash velocity is small compared with the speed of flow and provided that the mach number is sufficiently greater than. The elastic behaviour of the panel is given by von karman's large deflection equations modified to cover initially curved plates. The solution of the equations is carried out by means of galerkin's method, which has been shown to give valid results for a panel with a non-zero bending rigidity. The influence of the midplane compressive force carried by the panel itself, the initial buckle amplitude and the elastic restraint against edge displacements is investigated, and curves are presented giving the critical dynamic pressure ratio as a function of these variables.","url":"cran.html#doc894","title":"Flutter of a two dimensional simply supported buckled panel with elastic restraint against edge displacement."},
{"url":"cran.html#doc822","title":"Effects of imperfections on buckling of thin cylinders and columns under axial compression.","description":"Donnell, L.H. And Wan, C.C. J. App. Mech. 1950. Von karman and tsien have shown that under elastic conditions the resistance of perfect thin cylinders subjected to axial compression drops precipitously after buckling. It is considered that this indicates that this type of buckling is very sensitive to imperfections or disturbances. In this paper the effects of certain imperfections of shape turbances combined) are studied by the large-deflection shell theory developed in a previous paper (2). It is found that two types of buckling failure may occur. One is of a purely elastic type which occurs when the peak of the average stress versus average strain curve is reached, while the other type is precipitated by yielding, which for thicker cylinders or lower-yield material may occur before such a peak is reached. Curves are derived giving the dependence of each type of failure upon the dimensions and elastic and yield properties of the specimen and also upon an /unevenness factor/ u which determines the magnitude of the initial imperfections and is assumed to depend on the method of fabrication. The relations derived are in line with test results, and similar studies of the buckling of struts indicate that the magnitude of the initial imperfections which have to be assumed to explain test strengths are reasonable."},
{"description":"Willmarth, W.W. Rand corp. Rm.2078, 1957. Within the framework of linearized flow theory an equivalence between a fluid mass source, a heat source, and streamwise body forces is developed. The equivalence between the fluid mass source and heat source was first noticed by hicks(2) and later by chu. (3) using the equivalence the flow field produced by heat addition and by magnetohydrodynamical body forces can be computed. Examples for a two-dimensional flat plate, a delta wing, an axially symmetric slender body, and a wedge-shaped afterbody are computed at subsonic and supersonic speeds. The efficiency of lift or thrust production by surface heat addition is very low at subsonic speeds. At supersonic speeds the efficiency is compared with the efficiency of a conventional turbojet-powered aircraft configuration. It is found that the efficiency of lift or thrust production by heat addition on two-dimensional bodies is approximately the same as that for a turbojet-powered two-dimensional body. The efficiency is somewhat higher at low supersonic mach numbers and behaves as, decreasing to a constant value as increases. On the other hand, the efficiency of thrust production by heat addition increases linearly with mach number when heat is added on the rear surface of an axially symmetric afterbody of parabolic shape.","url":"cran.html#doc1328","title":"The production of aerodynamic forces by heat addition on external surfaces of aircraft."},
{"url":"cran.html#doc455","title":"Modified cross-lees mixing theory for supersonic separated and reattaching flows.","description":"Glick, H.S. Galcit hyp. Res. Proj. Memo 53, 1960. Re-examination of the crocco-lees method has shown that the previous quantitative disagreement between theory and experiment in the region of flow up to separation was caused primarily by the improper c(k) relation assumed. A new c(k) correlation, based on low-speed theoretical and experimental data and on supersonic experimental results has been developed and found to be satisfactory for accurate calculation of two-dimensional, laminar, supersonic flows up to separation. A physical model which incorporates the concept of the /dividing/ streamline and the results of experiment. According to this physical model, viscous momentum transport is the essential mechanism in the zone between separation and the beginning of reattachment, while the reattachment process is, on the contrary, an essentially inviscid process. This physical model has been translated into crocco-lees languages using a semiempirical approach, and approximate c(k) and f(k) relations have been determined for the separated and reattaching regions. The results of this analysis have been applied to the problem of shockwave, laminar-boundary-layer interaction, and satisfactory a study of separated and reattaching regions of flow has led to quantitative agreement with experiment has been achieved."},
{"description":"Antonio ferri and paul A. Libby Department of aeronautical engineering and applied mechanics, polytechnic institute of brooklyn, brooklyn, N.Y. According to the classical boundary-layer theory the flow about bodies at reynolds numbers of aeronautical interest can be considered as composed of two regimes.. An outside inviscid flow and a thin boundary-layer region adjacent to the body. This point of view leads to the approximation that, on a slightly curved surface, throughout the layer is negligibly small. The additional assumption that the inviscid flow is irrotational leads to the requirement that is zero at the outer edge of the boundary layer. In this theory any interaction between the two regimes is accountable by a simple correction to the body shape based on the boundary-layer displacement thickness. Recently, in connection with hypersonic laminar boundary layers, this classical point of view has been modified., an interaction between the two flow regimes leading to a self-induced axial pressure gradient has been considered. It is the purpose of the present note to point out another type of interaction which may be of practical importance and of fundamental interest even at mach numbers below those considered in the hypersonic boundary-layer theory and which may have to be considered in that theory.","url":"cran.html#doc134","title":"Note on an interaction between the boundary layer and the inviscid flow."},
{"description":"Morgan, H.G. And Miller, R.W. Nasa memo 4-8-59l, 1959. 2 in helium flow. Results of hypersonic flutter tests on some simple models are presented. The models had rectangular plan forms of panel aspect ratio 1.0, no sweepback, and bending-to-torsion frequency ratios of about. Two airfoil sections were included in the tests ,. Double wedges of 5-, 10-, and 15-percent thickness and flat plates with straight, parallel sides and beveled leading and trailing edges. The models were supported by a cantilevered shaft. The double-wedge wings were tested in helium at a mach number of 7.2. An effect of airfoil thickness on flutter speed was found, thicker wings requiring more stiffness to avoid flutter. A few tests in air at a mach number of 6.9 showed the same thickness effect and also indicated that tests in helium would predict conservative flutter boundaries in air. The data in air and helium seemed to be correlated by piston-theory calculations. Piston-theory calculations agreed well with experiment for the thinner models but began to deviate as the thickness parameter approached and exceeded 1.0. A few tests on flat-plate models with various elastic-axis locations were made. Piston-theory calculations would not satisfactorily predict the flutter of these models, probably because of their blunt leading edges.","url":"cran.html#doc686","title":"Flutter tests of some simple models at a mach number of 7. 2 in helium flow."},
{"url":"cran.html#doc623","title":"On the coupling between heat and mass transfer.","description":"Tewfik, O.E. J. Ae. Scs. 28, 1962, 1009. In mixtures of two different gases or liquids, one constituent will migrate spontaneously toward the warmer parts, and the other toward the colder parts. This phenomenon, known as the soret effect, and its converse the dufour effect, were discovered as early as 1856 and 1873 respectively. The two effects can also be considered as a simultaneous transport of mass and heat, or as a coupling between heat and mass transfer. The effects of this coupling have been neglected in all investigations of heat transfer in multicomponent flow systems so far, on the a priori assumption that they are small. In a recent publication however, it was shown that they can be large in laminar-boundary-layer-type flows with helium injection. Turbulent-boundary-layer measurements and an analysis conducted at the heat transfer laboratory clearly showed significant effects of the coupling on heat transfer and adiabatic wall temperature. From additional measurements, the results of which are presented below, it is possible to separate the heat flux at the model wall into one part depending on the temperature gradient and a second part caused by the coupling. It is shown that the latter exceeds the former, and hence the coupling may not be neglected a priori without careful consideration."},
{"url":"cran.html#doc1205","title":"Effects of cooling on boundary layer transition on a hemi- sphere in simulated hypersonic flow.","description":"Dunlap, R. And Kuethe, A.M. J. Ae. Scs. 1962, 1454. An experimental investigation of the effects of cooling on boundary-layer transition on a 9-in. Diameter hemisphere in simulated hypersonic flow is reported. The newtonian pressure distribution was obtained by use of a shroud and boundary layer cooling was achieved by internally cooling the model. Transition was detected with hot wires and with a pitot tube at the surface. Attained. Transition was observed in the subsonic and near-sonic flow region at and upstream of n = 45. In this region the stagnation reynolds number at which transition occurred when the surface was highly polished was only slightly affected by cooling within the temperature range. Thus, transition reversal does not occur on a polished spherical surface within the range of these tests, and we therefore conclude that the cooling did not cause the linear stability of boundary layer to decrease significantly. An essential feature of transition studies with boundary-layer cooling is the close control of surface roughness. In the present experiments this control required, in addition to a highly polished surface, the necessity for low water vapor dewpoint, the avoidance of carbon dioxide condensation and the utilzation of every available means for removing the dust from the airstream."},
{"title":"The flow field over blunted flat plates and its effect on turbulent boundary growth and heat transfer at a mach number of 4. 7.","url":"cran.html#doc1107","description":"Tendeland, T. Nasa tn.d689, 1961. 7. Surface pressures, impact and static pressure distributions in the flow field over the plate, and local heating rates were measured on a flat plate with various leading-edge diameters. The tests were conducted at a mach number of 4.7 and a free-stream reynolds number of 3.8x10 per foot. It was found that the shape of the shock wave indicated the existence of an outward deflection of the flow over the plate. The flow deflection caused an outward deflection of the shock-wave asymptote of approximately the shock-wave angle calculated including boundary-layer growth. The mach number distributions in the shear layer evaluated from pitot and static pressure surveys agreed with predictions based on shock-wave shape. The predicted turbulent heat-transfer coefficients for the blunted flat plates agreed with the measured heat-transfer coefficients. A comparison between the measured heat-transfer coefficients for the blunted flat plates and the calculated coefficients for a sharp leading-edged plate indicated that the coefficients were highest near the leading edge of the most blunted plate. The measured heat-transfer coefficients dropped to approximately 80 percent of the sharp-plate values at a considerable distance from the leading edge for all of the blunted flat plates."},
{"description":"Willi F. Jacobs Lockheed aircraft corporation, georgia division Exact conical-flow solutions are available only for circular cones at zero angle of attack. For nonaxisymmetric cones or cones at angle of attack, only approximate methods exist. These methods are generally quite complicated and further limited to certain body shapes or certain mach-number ranges. A great need was therefore felt for a simple approximate method applicable to any arbitrarily shaped conical body at zero incidence as well as at angle of attack. Such a method has been developed recently at lockheed and is presented here in abbreviated form. The method is based on the /equivalent-cone/ theory. This theory determines the pressure on a conical body utilizing information for a symmetric cone at zero angle of attack with the same normal component of the free stream with respect to the surface as the local element of the body considered. This method works relatively well at high mach numbers. However, it is quite inconsistent at lower mach numbers, especially for bodies which deviate considerably from circular cones. The equivalent-cone method does not give satisfactory results, mainly due to the fact that it considers only the local surface element on the body independent of the other body elements in the newtonian-theory manner.","url":"cran.html#doc122","title":"A simplified approximate method for the calculation of the pressure around conical bodies of arbitrary shape in supersonic and hypersonic flow."},
{"description":"Garrick, I.E. Proc. 5th int. Cong. App. Mech. 1938, J. Wiley, 590. The growth of lift on a airfoil starting impulsively from rest to a uniform velocity has been given by wagner (1925). The steady-state lift due to circulation on an airfoil oscillating sinusoidally and moving with uniform velocity has been given by theodorsen the present paper based essentially on the material of N. A. C. A. Report no. 629 by the author, discusses some reciprocal relations of the nature of fourier transforms existing between the functions of wagner and theodorsen. Kussner (1936) has already shown that wagner's function may be derived from theodorsen's function. By means of a superposition principle it is possible to utilize these fundamental functions to treat general problems in transient expression which is accurate to within 2 percent is given for wagner's function. This expression leads to a good approximate expression for theodorsen's function in terms of the exponential integral, instead of hankel functions. An analogy is drawn between transient hydrodynamic flows and transient electrical flows. Kussner (1936) has introduced a function describing the growth of lift on an airfoil entering a sharp edged vertical gust region. This function bears a certain relation to wagner's function which is briefly discussed.","title":"On some fourier transforms in the theory of non-stationary flows.","url":"cran.html#doc1330"},
{"url":"cran.html#doc628","title":"Thermal effects on a transpiration cooled hemisphere.","description":"Gollnick, A.F. J. Ae. Scs. 29, 1962, 583. An approximate method is used to obtain the injection distribution which would exist on an isothermal, transpiration-cooled hemisphere in a supersonic stream. This distribution is the same for both air and helium injection, and is independent of the blowing level. A model having this distribution was tested in the naval supersonic laboratory wind tunnel at a mach number of 3.53. It is concluded that the design technique is reasonably accurate. Data taken near the nose are compared with the theories for air and helium injection. The agreement in the case of the reduction in heat-transfer coefficient is good. The values of insulated wall temperature obtained near the nose with helium injection are 8 percent above the local stagnation temperature, and largely independent of injection rate. It is believed that this phenomenon may be attributed to the thermal diffusion of the helium within the boundary layer. Air injection causes a slight reduction in the insulated wall temperature. It is shown that injection of either air or helium at the hemisphere nose considerably reduces the heat flux at the surface. The additional reduction in heat flux resulting from helium injection as opposed to air injection, and predicted by existing theory, is largely absent."},
{"title":"Stability derivatives of cones at supersonic speeds.","url":"cran.html#doc814","description":"Tobak, M. And Wehrend, W.R. Naca tn.3788, 1956. The aerodynamic stability derivatives due to pitching velocity and vertical acceleration are calculated by use of potential theory for circular cones traveling at supersonic speeds. The analysis is based on two theoretical techniques used successfully previously in application to the case of uniform axial and inclined flow. In the first, potential solutions for axial flow and crossflow are derived from the first-order wave equation but in application to calculations for the forces no approximations are made either to the tangency condition or to the isentropic pressure relation. The second method consists in combining the first-order crossflow potential with an axial-flow potential correct to second order. Closed-form solutions by both methods are found for a cone, and numerical results for the stability derivatives are presented as a function of mach number for cones having semivertex angles of 10 and 20. In addition, expressions for the forces, moments, and stability derivatives of arbitrary bodies of revolution are obtained using newtonian impact theory. Numerical results for cones compare well with those obtained from the combined first- and second-order potential theory at the highest mach number for which the latter theory is applicable."},
{"title":"Non-equilibrium expansions of air with coupled chemical reactions.","url":"cran.html#doc1296","description":"Eschenroeder, A.Q., boyer, D. And Hall, J.G. Phys. Fluids, 1962. Analysis and solutions of the streamtube gas dynamics involving coupled chemical rate equations are carried out. Results are presented for airflows along the surface of blunt bodies and through hypersonic nozzles. Speeds and altitudes corresponding to re-entry were selected to obtain initial conditions for the external flow calculations. Conditions appropriate to hypersonic tunnel testing were chosen for the nozzle flow calculations. Composition histories are shown for a kinetic mechanism including 6 species and 14 reactions. Gas-dynamic effects of nonequilibrium processes qualitatively resemble those reported earlier. However, the freezing process is complicated by the coupling of the nitric oxide shuffle reactions with the dissociation-recombination reactions. In many cases of hypersonic nozzle flows where the energy in nitrogen dissociation is significant, the fast shuffle reactions prevent nitrogen-atom freezing which would otherwise occur if three-body recombination were the only process operating. Nitric oxide concentrations undershoot the equilibrium values if the ratio of nitric oxide to oxygen molecule concentrations exceeds unity in the freezing region. This depletion of nitric oxide leads to nitrogen-atom freezing."},
{"title":"Jet effects on base pressure of conical afterbodies at mach 1. 91 and 3. 12.","url":"cran.html#doc282","description":"Baughman, L.E. And Kochendorfer, F.D. Naca rm e57e06. 91 and 3. 12. Data are presented which show the effect of a jet on base pressure for a series of conical afterbody-jet-nozzle combinations having boat-tail angles that varied from 0 to 11 and base-to-jet diameter ratios that varied from 1.11 to 2.67. The jet nozzles had exit angles from 0 to 20 and were designed for exit mach numbers from 1.0 to 3.2. Pressure ratios up to 30 were tested for both a cold (air) and a hot numbers of 1.91 and 3.12. In general, base pressure increased for increasing values of boat-tail angle, nozzle angle, jet temperature, and jet total pressure and for decreasing values of base-to-jet diameter ratio, jet mach number, and free-stream mach number. The addition of tail surfaces produced only small changes in base pressure. For all variables, base pressure is governed by the maximum pressure rise that can be supported by the wake fluid in the region of the trailing shock. The wake pressure ratio is in turn governed by the jet and free-stream mach numbers adjacent to the wake region and by the state of the boundary layer on the boattail and on the nozzle. Values of wake pressure ratio computed using the theory of korst, page, and childs were in good agreement with experimental values for convergent nozzles."},
{"title":"Experimental studies of flutter of buckled rectangular panels at mach numbers from 1. 2 to 3. 0 including effects of pressure differential and of panel width-length ratio.","url":"cran.html#doc857","description":"Sylvester, M.A. Nasa tn.d833, 1961. 2 to 3. 0 including effects of pressure differential and of panel width-length ratio. Experimental panel flutter data have been obtained at mach numbers from 1.2 to 3.0 for buckled rectangular panels and the effect of a pressure differential has been determined. Increasing the pressure differential was effective in eliminating flutter on most of the panels tested. The effects of the variables in the panel flutter parameter sure, e is young's modulus, and t and l are the panel thickness and length, respectively) were investigated for buckled panels clamped on the front and rear edges and a critical value of this parameter of 0.44 is indicated at zero pressure differential when the panel width-length ratio is 0.69. An estimated flutter boundary is presented for buckled panels clamped on four edges, with width-length ratios of 0.21 to 4.0. This boundary shows that the panel width is more significant than the panel length when the ratio of width to length is less than approximately 0.5. Panels clamped on four edges and buckled in two half waves in the direction of flow were found to be particularly susceptible to flutter. The results of limited tests on panels with applied damping, curvature, and lengthwise stiffeners are also presented and discussed."},
{"description":"Pinkerton, R. M. Naca R. 563, 1936. Pressures were simultaneously measured in the variable-density tunnel at 54 orifices distributed over the midspan section of a 5 by 30 inch rectangular model of the N.A.C.A. 4412 airfoil at 17 angles of attack ranging from -dash 20degree to 30degree at a reynolds number of approximately 3, 000, 000. Accurate data were thus obtained for studying the deviations of the results of potential-flow theory from measured results technique are presented. It is shown that theoretical calculations made either at the effective angle of attack or at a given actual lift do not accurately describe the observed pressure distribution over an airfoil section. There is therefore developed a modified theoretical calculation that agrees reasonably well with the measured results of the tests of the N.A.C.A. 4412 section and that consists of making the calculations and evaluating the circulation by means of the experimentally obtained lift at the effective angle of attack,. I.E., the angle that the chord of the model makes with the direction of the flow in the region of the section under consideration. In the course of the computations the shape parameter is modified, thus leading to a modified or an effective profile shape that differs slightly from the specified shape.","url":"cran.html#doc443","title":"Calculated and measured pressure distributions over the midspan section of the naca 4412 airfoil."},
{"title":"Axisymmetric magnetohydrodynamic channel flow.","url":"cran.html#doc1222","description":"Hains, F.D. And Holer, Y.A. J. Ae. Scs. 1962, 143. The axisymmetric subsonic and supersonic flow fields, and the skin friction and heat transfer of an electrically conducting compressible fluid flowing in a channel of constant circular area through a magnetic field are investigated when the magnetic reynolds number is small. The inviscid-flow field for flow through a dipole field is solved by the method of characteristics in the supersonic case. For the subsonic case, linearized equations are derived for small values of the magnetic interaction parameter. Numerical results are obtained by the relaxation method. The inviscid-flow-field solutions are used as boundary conditions for the laminar boundary layer along the wall, in which axial pressure gradients form an important feature. The exact continuum-flow equations are reduced by an order-of-magnitude analysis to the boundary-layer equations, which are solved numerically by an integral method using a fourth-degree velocity profile and a fifth-degree stagnation-enthalpy profile. Pressure, temperature, and heat-transfer measurements are made with a shock tube under supersonic-flow conditions closely approaching those used in the numerical computations. General agreement is found between the theoretical and the experimental results."},
{"description":"Gundersen, R.M. J. Ae. Scs. 1962, 1421. An initially uniform magnetohydrodynamic shock wave of arbitrary strength propagates through a channel which consists of two portions of which one has uniform cross-sectional area while the other is of varying cross-sectional area. It is assumed that the flow in the nonuniform section in front of the shock is initially a uniform state and no perturbations (due to the area variations) of this flow reach the shock until the area variation is encountered. When the shock enters the nonuniform section, it is perturbed, the shock strength altered and the subsequent flow is nonisentropic. In addition to the perturbation due to the effect of the area variations on the initially uniform upstream flow, there are two further contributions--viz., a permanent perturbation caused directly by the area changes and a transient disturbance--which propagates with true sonic speed with respect to the flow behind the shock, due to reflections of the permanent perturbation at the shock. Expressions for these various contributions are obtained. The results presented include as special cases propagation of a nonuniform conventional gas dynamic shock into a moving nonconduction fluid and propagation of a nonuniform hydromagnetic shock wave into a stationary fluid.","url":"cran.html#doc1203","title":"The propagation of a nonuniform magnetohydrodynamic shock wave into a moving monatomic fluid."},
{"description":"Livingood, J.N.B. And Donoughe, P. Naca tn.3588, 1955. A summary of exact solutions of the laminar-boundary-layer equations for wedge-type flow, useful in estimating heat transfer to such arbitrarily shaped bodies as turbine blades, is presented. The solutions are determined for small mach numbers and a prandtl number at the wall of 0.7 ,. Ranges of mainstream pressure gradients and rates of coolant flow through a porous wall are considered for the following cases.. (1) small temperature changes in the boundary layer along a constant- and along a variable-temperature wall, and (2) large temperature changes in the boundary layer along a constant-temperature wall. Dimensionless forms of heat-transfer and friction parameters and boundary-layer thicknesses are tabulated. The results indicate that coolant emission and increased stream-to-wall temperature ratios diminished the friction and heat transfer for a constant wall temperature. For a variable wall temperature with small temperature differences in the boundary layer, the friction was unaffected, but the heat transfer was greatly increased for increased wall-temperature gradient. Heat-transfer results in the literature reveal that transpiration cooling is much more effective for prandtl numbers of the order of 5.0 than for 0.7.","title":"Summary of laminar boundary layer solutions for wedge-type flow over convection and transpiration cooled surfaces.","url":"cran.html#doc661"},
{"description":"Watkins, C.E. And Runyal, H.L. And Woolston, D.S. Naca rep. 1234, 1955. This report treats the kernel function of an integral equation that relates a known or prescribed downwash distribution to an unknown lift distribution for a harmonically oscillating finite wing in compressible subsonic flow. The kernel function is reduced to a form that can be accurately evaluated by separating the kernel function into two parts.. A part in which the singularities are isolated and analytically expressed and a nonsingular part which may be tabulated. The form of the kernel function for the sonic case /mach number of 1/ is treated separately. In addition, results for the special cases of mach number of o /incompressible case/ and frequency of o /steady case/ are given. The derivation of the integral equation which involves this kernel function, originally performed elsewhere /see, for example, naca technical memorandum 979/, is reproduced as an appendix. Another appendix gives the reduction of the form of the kernel function obtained herein for the three-dimensional case to a known result of possio for two-dimensional flow. A third appendix contains some remarks on the evaluation of the kernel function, and a fourth appendix presents an alternate form of expression for the kernel function.","title":"On the kernel function of the integral equation relating the lift and downwash distributions of oscillating finite wings in subsonic flow.","url":"cran.html#doc705"},
{"url":"cran.html#doc991","title":"Wing-flow study of pressure drag reduction at transonic speed by projecting a jet of air from the nose of a prolate spheroid of fineness ratio 6.","description":"Lopatoff, M. Naca rm l51e09, 1951. A study was made at transonic speeds by the naca wing-flow method of the pressure-drag reduction obtained by projecting a high-energy jet of air from the nose of a prolate spheroid. Supplementary information was obtained by taking shadowgraphs of the model mounted in a small supersonic tunnel at a constant mach number of 1.5. The high-velocity jet was observed to alter the pressure distribution over the body in such a way that the pressure drag of the body was reduced,. Thus, in a restricted sense, the nose jet produced a thrust on the body. Under the conditions investigated, the thrust produced by the nose jet was never so large as that which would be expected from a conventional rearward jet. For example, under the best conditions tested /mach number of 1.07/ the reduction in body pressure drag caused by the nose jet more than compensated for the negative thrust of the jet itself. However, the magnitude of the net reduction in drag /change in body pressure drag with jet on and jet off minus the adverse thrust of the jet/ was only about one-half of the thrust which would be produced by the same jet exhausting rearward. The appearance of such an unexpectedly large effect in the first trial indicated the phenomenon to be worth further study."},
{"description":"Gerard, G. J. Ae. Scs. 29, 1962. In a recent paper lee treated the complex problem of the plastic buckling and postbuckling behavior of an axially compressed cylindrical shell containing initial imperfections, representing an important step forward in our understanding of this common, yet perplexing, structural element. Lee drew two major conclusions.. (a) even with initial imperfections the incremental theory of plasticity considerably overestimates the buckling strength as compared with the deformation theory, which is in substantially good agreement with experiments, and strength of cylindrical shells subject to axial compression are significant. It is the purpose of this note to discuss the second conclusion in terms of lee's experimental and theoretical results, other experimental data on inelastic buckling of 7075-t6 aluminum-alloy cylinders, and recent theoretical results on the inelastic buckling of cylinders in the axisymmetric and circumferential modes. In particular, this writer does not believe that lee has proved that initial imperfections are important for the group of cylinders that he has tested. On the contrary, it is believed that initial imperfections are completely insignificant for this group of cylinders although of probable significance in other cases.","title":"On the role of initial imperfections in plastic buckling of cylinders under axial compression.","url":"cran.html#doc1122"},
{"url":"cran.html#doc560","title":"A theoretical study of the effect of upstream transpiration-cooling on the heat transfer and skin friction characteristics of a compressible laminar boundary layer.","description":"Rubesin, M.W. And Inouye, M. Naca tn.3969, 1957. An analysis is presented which predicts the skin-friction and heat-transfer characteristics of a compressible, laminar boundary layer on a solid flat plate preceded by a porous section that is transpiration cooled. The analysis is restricted to a prandtl number of unity and linear variation of viscosity with temperature. The local skin friction has been found to have a low value in the region of transpiration cooling and then to increase until it approaches the value for a completely nonporous surface asymptotically. The initial increase in local skin friction is rapid as half of the ultimate increase occurs in a distance beyond the porous region that is about 20 percent of the length of the porous region for all rates of injection. When the total coolant flow rate is kept constant and the porous length is varied, it is found that the average skin friction on a partially porous plate is slightly lower than that on a fully porous plate. The local heat transfer behaves in a manner similar to that of the local skin friction. It is found, in an example, that the temperature at the end of a partially porous plate could be maintained at about the same temperature as a fully porous plate by doubling the total rate of coolant flow."},
{"description":"Hancock, G. J. Ae. Scs. 1959, 495. In part (1), as a first approach to a theoretical investigation of low aspect ratio rectangular plate wings of constant thickness, the two assumptions are made that.. (a) the spanwise form of the structural distortion is known, leaving the chordwise distortion arbitrary,. And (b) the aerodynamic forces are approximations of the supersonic linearized theory. The form of the chordwise distortion is then deduced from the differential equation representing the state of neutral equilibrium for small displacements at the critical divergence speed. Secondly, this problem is investigated using measured structural flexibility coefficients together with theoretical aerodynamic coefficients. Thirdly, the usual series solution based on the rayleigh-ritz approach is discussed, using the same assumptions as in the first method. All the results of these methods are consistent and indicate that the transonic regime at m = 1 is the most critical for divergence. In part (2), it is established that sweeping the leading edge of a plate airfoil of constant thickness increases its stability. For angles of sweep less than 30, the critical conditions occur when the leading edge is sonic, but for angles greater than 30 the critical conditions occur when m = 1.","url":"cran.html#doc1320","title":"Divergence of plate airfoils of low aspect ratio at supersonic speeds."},
{"title":"Air pressure on a cone moving at high speeds.","url":"cran.html#doc1303","description":"Taylor, G.I. And Maccoll, J.W. Proc. Roy. Soc. A, 139, 1933, 278. The cone is considered to be moving at a velocity higher than that of sound, so that there is in front of it a shock wave, moving with the same speed as the cone itself. In the first part of the paper, the case is investigated mathematically where the flow is irrotational, and the pressure, velocity and density of the air stream are each constant over the surfaces of cones coaxial with the moving solid cone. The complete solution is obtained in numerical form, for cones of semi-vertical angle of the paper, the results are compared with experiment, both in respect of pressure distribution as measured in a wind tunnel, and also (for the 30 cone) by comparison with photographs of bullets in flight. In the latter case the theory should only be applicable if the speed is 1.46 or more times the velocity of sound, and it is in fact found in the photographs, that the nature of the wave alters at about this velocity. The exact solution found, is compared with an approximation given recently by V. Karman and moore. This should be valid for thin spindle-shaped bodies, and does in fact agree well in the case of the cone of 10 semi-vertical angle, but diverges increasingly from the truth as the angle is increased."},
{"url":"cran.html#doc520","title":"Wing-tail interference as a cause of 'magnus' effects on a finned missile.","description":"Benton, E.R. J. Ae. Scs. 29, 1962, 1358. Wing-tail interference is shown to cause large /magnus/ effects on a finned missile whose wings are deflected into an aileron setting. A simple experimental method with water as the working medium is used to obtain low-speed magnus data on a rolling missile. The missile is a slender cruciform configuration with all-movable wings and fixed tail fins. Magnus data are presented for angles of attack up to 15 and for the one (high) roll rate which accompanies a 30 aileron deflection angle of the wings. Tests conducted at zero roll rate but with the wing deflection maintained, revealed large forces in the magnus direction, thereby providing the basis for understanding magnus effects due to wing-tail interference. A semiempirical theory is proposed to explain the experimental data. A simplified model of the wake behind the wings is introduced to predict tail-interference factors. Good agreement with the data is obtained. This magnus effect is opposite in direction to the classical magnus lift on a spinning cylinder ,. It is much larger than either that effect or the one on a missile with only one set of fins. Wing-tail interference is the predominant source of the effect ,. Roll rate only modifies the basic interference mechanism."},
{"description":"Mull, H.R. And Algranti, J.S. Nasa tn.d280, 1960. The results are presented for a flight test program using a fighter type jet aircraft flying at pressure altitudes of 10, 000, 20, 000, and apparatus was used to measure and record the output of microphones and hot-wire anemometers mounted on the forward-fuselage section and wing of the airplane. Mean-velocity profiles in the boundary layers were obtained from total-pressure measurements. The ratio of the root-mean-square fluctuating wall pressure to the free-stream dynamic pressure is presented as a function of reynolds number and mach number. The longitudinal component of the turbulent-velocity fluctuations was measured, and the turbulence-intensity profiles are presented for the wing and forward-fuselage section. In general, the results are in agreement with wind-tunnel measurements which have been reported in the literature. For example, the variation of (is the root mean square of the wall-pressure fluctuation, and q is the free-stream dynamic pressure) with reynolds number was found to be essentially constant for the forward fuselage-section boundary layer, while variations at the wing station were probably unduly affected by the microphone diameter, which was large compared with the boundary-layer thickness.","title":"Flight measurement of wall pressure fluctuations and boundary-layer turbulence.","url":"cran.html#doc76"},
{"description":"Adams, G.J. And Dugan, D.W. Naca r1088, 1952. A method of analysis based on slender-wing theory is developed to investigate the characteristics in roll of slender cruciform wings and wing-body combinations. The method makes use of the conformal mapping processes of classical hydrodynamics which transform the region outside a circle and the region outside an arbitrary arrangement of line segments intersecting at the origin. The method of analysis may be utilized to solve other slender cruciform wing-body problems involving arbitrarily assigned boundary conditions. In the present report, the application of the method has shown.. Differential incidence of both pairs of opposite surfaces of the cruciform wing-body combinations are practically independent of the body-diameter-maximum-span ratio up to a value of this ratio of 0.3. Arrangement is only 62 percent greater than that for a corresponding planar wing-body combination. Dence of both pairs of the opposing surfaces of the cruciform wing-body arrangement, is only 52 percent greater than that for a corresponding planar wing-body combination. Unit surface deflection) of the cruciform wing-body arrangement having four equally deflected panels is therefore 94 percent of the corresponding planar wing-body combination.","title":"Theoretical damping in roll and rolling moment due to differential wing incidence for slender cruciform wings and wing-body combinations.","url":"cran.html#doc432"},
{"description":"Dorrance, W.H. J. Ae. Scs. 161, 43. The concurrent approach to chemical and vibrational equilibrium of a pure diatomic gas passing through a strong normal shock wave is investigated. It is demonstrated that the equilibrium degree of dissociation behind the shock front, and hence the density, for the case where the vibrational degrees of freedom are frozen out can exceed the degree of dissociation, and hence the density, for the case where all degrees of freedom are in equilibrium. Thus the necessary condition for a maximum of the density between the shock front and the position of full equilibrium flow downstream of the shock front is established. The sufficient condition that such a maximum be observable is shown to be that the approach to equilibrium of the vibrational degrees of freedom (or any other internal degrees of freedom) must lag the approach to dissociation equilibrium by a significant amount,. That is, there must be at least an order of magnitude difference in the respective relaxation times before such a maximum might be observed. An example calculation for a mach 13 strong shock wave in oxygen illustrates the appearance of such a maximum of the density and its dependency upon the relative values of the vibration and dissociation relaxation times.","title":"On the approach to chemical and vibrational equilibrium behind a strong normal shock wave.","url":"cran.html#doc1252"},
{"description":"Woolston, D.C. And Castile, G.E. Naca tn.2558, 1951. An experimental investigation has been made of some effects of variations in several parameters, including fluid density, on the flutter characteristics of light uniform cantilever wings. The assortment of wings tested covered a variety of positions of the elastic axis and center of gravity and values of the aspect ratio of 8, 6, and 4. The relative-density parameter (where k is representative of the ratio of fluid density to wing mass) was varied over a range of values from 1.2 to nearly 14. Special emphasis has been placed on the lower values. The experimental investigation has been supplemented by an analytical investigation based on the two-dimensional aerodynamic theory for incompressible flow. In a few instances corrections for the effects of finite span have been made. In general, the theoretical results followed the trends indicated by experiment except at very low values of the relative-density parameter. For these low values the analytical considerations employed indicated a freedom from flutter not found experimentally. At higher values of the flutter-speed coefficient is shown to decrease with decreasing values of and to be nearly proportional to the inverse of the square root of the air density.","title":"Some effects of variations in several parameters including fluid density on the flutter speed of light uniform cantilever wings.","url":"cran.html#doc442"},
{"description":"Nitzburg, G.E. And Crandall, S. Naca tn.1813, 1949. A study of experimental pressure distributions and section characteristics for several moderately thick airfoil sections was made. A correlation appears to exist between the drag-divergence mach number and the free-stream mach number for which sonic velocity occurs at the airfoil crest, the chordwise station at which the airfoil surface is tangent to the free-stream direction. It was found that, since the mach number for which sonic velocity occurs at the airfoil crest can be estimated satisfactorily by means of the prandtl-glauert rule, a method is provided whereby the drag-divergence mach number of an airfoil section at a given angle of attack can be estimated from the low-speed pressure distribution and the airfoil profile. This method was used to predict with a reasonable degree of accuracy the drag-divergence mach number of a considerable number of airfoil sections having diverse shapes and a wide range of thickness-chord ratios. The pressure distributions and section force characteristics of several moderately thick airfoil sections at mach numbers above the drag-divergence mach number were analyzed. Some of the characteristics of the flow over these airfoils at supercritical mach numbers are discussed.","title":"A study of flow changes associated with airfoil section drag rise at supercritical speeds.","url":"cran.html#doc70"},
{"description":"Ribner, H.S. Utia r51, 1958. The spatial distribution of noise sources along a jet is investigated by application of lighthill's theory to regions of 'similar' profiles. The analysis refers to the noise power emitted by a 'slice' of jet (section between two adjacent planes normal to the axis) as a function of distance x of the slice from the nozzle. It is found that this power is essentially constant with x in the initial mixing region (x law), then further downstream (say 8 or 10 diameters from the nozzle) falls off extremely fast (x law or faster) in the fully developed jet. Because of this striking attenuation of strength with distance, it is concluded that the mixing region produces the bulk of the noise and must dominate in muffler behavior,. Conversely, the 'fat' part of the jet must contribute much less to the total noise power than is commonly supposed. Powell's experiments on the effects of nozzle velocity profile on total noise power are interpreted qualitatively. The behavior of multiple-nozzle or corrugated mufflers, both as to overall quieting and frequency-shifting, is also interpreted in the light of the results. The possibility emerges that such mufflers may be improved without serious thrust loss by the addition of a sound-attenuating shroud.","url":"cran.html#doc219","title":"On the strength distribution of noise sources along a jet."},
{"description":"Maglieri, D.J., hubbard, H.H. And Lansing, D.L. Nasa tn.d48, 1959. 4 and at altitudes to 45, 000 feet. Time histories of noise pressures near ground level were measured during flight tests of fighter-type airplanes over fairly flat, partly wooded terrain in the mach number range between 1.13 and 1.4 and at altitudes from 25, 000 to 45, 000 feet. Atmospheric soundings and radar-tracking studies were made for correlation with the measured noise data. The measured and calculated values of the pressure rise across the shock wave were generally in good agreement. There is a tendency for the theory to overestimate the pressure at locations remote from the track and to underestimate the pressures for conditions of high tailwind at altitude. The measured values of ground-reflection factor averaged about 1.8 for the surfaces tested as compared to a theoretical value of 2.0. Two booms were measured in all cases. The observers also generally reported two booms,. Although, in some cases, only one boom was reported. The shock-wave noise associated with some of the flight tests was judged to be objectionable by ground observers, and in one case the cracking of a plate-glass store window was correlated in time with the passage of the airplane at an altitude of 25, 000 feet.","title":"Ground measurements of the shock wave noise from airplanes in level flight at mach numbers to 1. 4 and at altitudes to 45, 000 feet.","url":"cran.html#doc805"},
{"url":"cran.html#doc993","title":"The extent of the jet interference flow fields. Jet effects on cylindrical afterbodies housing sonic and supersonic nozzles which exhaust against a supersonic stream at angles of attack from 90degree to 180degree.","description":"Hayman, L.O. And Mcdearmon, R.W. Jet effects on cylindrical afterbodies housing sonic and supersonic nozzles which exhaust against a supersonic stream at angles of attack from 90degree to 180degree. An investigation has been made to determine jet effects on cylindrical afterbodies housing sonic and supersonic nozzles which exhaust against a supersonic stream at angles of attack from 90 to 180. The tests were conducted at a free-stream mach number of 2.91 and at free-stream reynolds numbers, based on body diameter, of 0.15x106 and stream static pressure investigated was from jet off to about 400. The data presented herein showed that, in general, variation of the ratio of jet total pressure to free-stream static pressure, jet-exit mach number, and ratio of jet-exit diameter to body diameter had large influences on the body pressures on the windward halves of the after-bodies and negligible influences on the leeward pressures. There was a negligible effect of reynolds number on the body pressures. The ratio of jet total pressure to free-stream static pressure also had a large influence on the base pressures at all angles of attack. Schlieren studies showed details of the shock-wave structure caused by the jet and the extent of the jet interference flow fields."},
{"description":"Yates, E.C. Naca rm l57l10, 1958. A method has been developed for calculating flutter characteristics of finite-span swept or unswept wings at subsonic and supersonic speeds. The method is basically a rayleigh type analysis and is illustrated with uncoupled vibration modes although coupled modes can be used. The aerodynamic loadings are based on distributions of section lift-curve slope and local aerodynamic center calculated from three-dimensional steady-flow theory. These distributions are used in conjunction with the /effective/ angle-of-attack distribution resulting from each of the assumed vibration modes in order to obtain values of section lift and pitching moment. Circulation functions modified on the basis of loadings for two-dimensional airfoils oscillating in a compressible flow are employed to account for the effects of oscillatory motion on the magnitudes and phase angles of the lift and moment vectors. Flutter characteristics have been calculated by this method for 12 wings of varying sweep angle, aspect ratio, taper ratio, and center- of-gravity position at mach numbers from 0 to as high as 1.75. Comparisons of the results with experimental flutter data indicate that this method gives generally good flutter results for a broad range of wings.","url":"cran.html#doc1339","title":"Calculation of flutter characteristics for finite-span swept or unswept wings at subsonic and supersonic speeds by a modified strip analysis."},
{"title":"Interference between the wings and tail plane of a slender wing-body tailplane combination.","url":"cran.html#doc230","description":"Owen, P.R. And Maskell, E.C. Rae R.aero.2441, 1951. An approximate method of predicting the interference between the wings and the tailplane of a slender wing-body-tailplane combination in an inviscid flow is developed, in order to explain the change in centre of pressure position with incidence which has been found to occur in wind tunnel and flight tests on guided weapons. Incidence changes in one plane only, normal to the plane containing the wings and the tail surfaces, have been considered. The method is based on slender body theory and the assumption that the wing trailing vortices roll-up completely before they reach the tailplane,. It is, therefore, applicable to weapons equipped with low aspect ratio wings far separated from the tail surfaces. When the tail surfaces are triangular and of low aspect ratio, an analytical solution is given for the effect of the wing downwash field on the tail lift. For high aspect ratio, rectangular tail surfaces it is suggested by comparison with experimental data, that the tail lift may be estimated approximately from the value of the mean downwash angle across the tail span. A summary of the method is given in para.5 which, in conjunction with the introduction, may be read independently of the rest of the report."},
{"description":"Reed, W.H. And Bland, S.R. Nasa tn.d659, 1961. An analytical investigation is made of a precession-type instability which can occur in a flexibly supported aircraft-engine-propeller combination. By means of an idealized mathematical model which is comprised of a rigid power-plant system flexibly mounted in pitch and yaw to a fixed backup structure, the conditions required for neutral stability are determined. The paper also examines the sensitivity of the stability boundaries to changes in such parameters as stiffness, damping, and asymmetries in the engine mount, propeller speed, airspeed, mach number, propeller thrust, and location of pitch and yaw axes. Stability is found to depend strongly on the damping and stiffness in the system. With the use of nondimensional charts theoretical stability boundaries are compared with experimental results obtained in wind-tunnel tests of an aeroelastic airplane model. In general, the theoretical results, which do not account for wing response, show the same trends as observed experimentally,. However, for a given set of conditions calculated airspeeds for neutral stability are consistently lower than the measured values. Evidently, this result is due to the fact that wing response tends to add damping to the system.","title":"An analytical treatment of aircraft propeller precession instability.","url":"cran.html#doc78"},
{"description":"J. F. W. Crane X 7 in. Hypersonic wind tunnel at R.A.E. Farnborough part ii. Heater performance. Tests on the storage heater, which is cylindrical in form and mounted horizontally, show that its performance is adequate for operation at m=6.8 and probably adequate for flows at m=8.2 with the existing nozzles. In its present state, the maximum design temperature of 680 degrees centigrade for operation at m=9 cannot be realised in the tunnel because of heat loss to the outlet attachments of the heater and quick-acting valve which form, in effect, a large heat sink. Because of this heat loss there is rather poor response of stagnation temperature in the working section at the start of a run. It is hoped to cure this by preheating the heater outlet cone and the quick-acting valve. At pressures greater than about 100 P.S.I.G. Free convection through the fibrous thermal insulation surrounding the heated core causes the top of the heater shell to become somewhat hotter than the bottom, which results in /hogging/ distortion of the shell. This free convection cools the heater core and a vertical temperature gradient is set up across it after only a few minutes at high pressure. Modifications to be incorporated in the heater to improve its performance are described.","url":"cran.html#doc603","title":"The 7 in. X 7 in. Hypersonic wind tunnel at R.A.E. Farnborough part ii. Heater performance."},
{"title":"Heat transfer to flat plate in high temperature rarefied ultra-high mach number flow.","url":"cran.html#doc571","description":"Nagamatsu, H.T., weil, H.A. And Sheet, R.E. Ars J. 32, 1962, 533. An investigation was conducted in a hypersonic shock tunnel to determine the local heat transfer rates for a sharp leading edge flat plate. The free stream mach number range was 7.95 to 25.1 with stagnation temperatures of approximately 2550 and 6500 R. For these temperature and mach number conditions, the strong interaction parameter, varied from 2.35 to 826. The corresponding knudsen numbers, based on the ratio of the free stream mean free path and the leading edge thickness, varied from 0.38 to 85.5. For free stream mach numbers greater than 10, knudsen numbers of approximately unity, and perfect gas conditions, the calculated heat transfer coefficients were found to vary as as predicted by the noninsulated flat plate theory of li and nagamatsu. For the case of, the leading edge slip phenomenon drastically reduced the local heat transfer coefficients as compared to the theoretical values predicted with no slip at the surface. For the extreme case of and, the measured local heat transfer rate was an order of magnitude less than the analytical value. Both the knudsen number and the free stream mach number are important physical parameters that determine the extent of the slip-flow region."},
{"description":"Mori, Y. Int. Devel. In heat transfer, 1961. Combined free and forced convective heat transfer in vertical channels has been studied by many researchers. Due to the need for engineering design information there have been many papers concerning cases of fully developed flow with varying wall temperature. Forced flows in a channel of electrically conducting fluid with a transverse magnetic field have been studied and the large effects of a magnetic field on the flow pattern have been established. Flows of combined free and forced convection in electrically conducting fluids in vertical channels with a transverse magnetic field are expected to attract attention in future engineering applications, for example, in a magneto-hydrodynamic generator or in plasma studies. However, except for a report by gershuni and zhukhovitskii (1) concerning a particular case, no general study has been published. This paper is a general treatment of fully developed, free and forced convective, laminar, magneto-hydrodynamic flow in a vertical channel with a transverse magnetic field. It includes combined free and forced convective flows in channels without a magnetic field reported by ostrach (2), tao (3), etc. As special cases. Hartmann flow (4) is included in the other limit.","title":"On combined free and forced convection laminar magnetohydrodynamic flow and heat transfer in channels with transverse magnetic field.","url":"cran.html#doc270"},
{"title":"On turbulent lubrication.","url":"cran.html#doc115","description":"Constantinescu, V.N. Proc.inst.mech.E. 173, 1959, 881. The paper concerns the hydrodynamic turbulent motion in the lubricant layer. Proceeding from the reynolds equations and introducing the approximations currently used in lubrication problems, owing to the lubricant film thickness, the general motion equations for turbulent lubrication are written. Using the prandtl mixing length hypothesis, exact and approximate solutions are obtained for the velocity distribution into the lubricant layer. The results are discussed by pointing out the pressure gradient and the reynolds number influence on the velocity distributions, as well as the differences with respect to the laminar flow. In order to obtain simple formulae, the exact dependence of the rate of flow on the pressure gradient into a dimensionless form is replaced by a linear relation, the slope of which depends on the reynolds number. This approximation allows the obtainment of the pressure differential equation under a simple form. The pressure equation is integrated in case of journal bearings, by assuming a constant or a variable viscosity of the lubricant. The results are compared to the experimental data obtained by M. I. Smith and D. D. Fuller and the good qualitative agreement is pointed out."},
{"title":"A theory of asymmetric hypersonic blunt-body flows.","url":"cran.html#doc1179","description":"Swigart, R.J. Aiaa jnl. 1963, 1034. Two-dimensional asymmetric and three-dimensional inviscid blunt-body flows are analyzed using a new method. The method is inverse, that is, the shock-wave shape and freestream conditions are taken as known, and the body shape and flow field are to be determined. Results at zero angle of attack are obtained as a special case of the general problem. Solutions at zero angle are calculated for a variety of body shapes at freestream mach numbers ranging from infinity to 1.85. The ratio of specific heats, is taken as 1.4. Comparison with results obtained using van dyke's and garabedian's numerical solutions indicates that the method under consideration is more accurate than the van dyke method for determining stand-off distance. Solutions are obtained for parabolic and paraboloidal shock waves at small angle of attack and infinite freestream mach number,. Assumes the values 1.4, 1.2, 1.1, and 1.05. For all cases, the streamline that wets the body passes through the shock wave slightly above the point where the shock is normal and thus does not possess maximum entropy. These results provide counter examples to the conjecture that any isolated convex body in a supersonic stream is wetted by the streamline of maximum entropy."},
{"description":"Lambourne, N.C. Arc 21, 844, 1960. The practical need for research into the aerodynamics of slender delta wings in unsteady motion has been emphasized in a recent paper by zbrozek. Two important aspects are.. - formation and presence of leading-edge vortices. With oscillatory or transient modes of longitudinal (or chordwise) bending. The first of the aspects above, has already been briefly discussed in ref. 2. One feature of the flow with leading-edge vortices which seems to be of particular significance to the dynamic behaviour of a wing is the shedding of vorticity at the leading edge as well as at the trailing edge. Any time-dependent motion, or distortion, of the wing leads to a change in the rate at which vorticity is shed. With more conventional types of flow, the free vorticity being shed only from the trailing edge has diminishing influence on the wing, but when the free vorticity is shed from the leading edge, in passing downstream, it remains close to the upper surface of the wing. It might be expected then, that, although the magnitudes of the unsteady forces may not be greatly affected for a slender delta, the time delays associated with the forces may be significantly different for the attached and separated regimes of leading-edge flow.","title":"Some current and proposed investigations into the flow for slender delta and other wings in unsteady motion.","url":"cran.html#doc902"},
{"description":"Pappas, C.C. And Okuno, A.F. J.aero.scs. 27, 1960, 321. Measurements of average skin friction of the turbulent boundary layer have been made on a 15 total included angle cone with foreign gas injection. Measurements of total skin-friction drag were obtained at free-stream mach numbers of 0.3, 0.7, 3.5, and x 10 with injection of helium, air, and freon-12 through the porous wall. Substantial reductions in skin friction are realized with gas injection within the range of mach numbers of this test. The relative reduction in skin friction is in accordance with theory--that is, the light gases are most effective when compared on a mass flow basis. There is a marked effect of mach number on the reduction of average skin friction,. This effect is not shown by the available theories. Limited transition location measurements indicate that the boundary layer does not fully trip with gas injection but that the transition point approaches a forward limit with increasing injection. The variation of the skin-friction coefficient, for the lower injection rates with natural transition, is dependent on the flow reynolds number and type of injected gas,. And At the high injection rates the skin friction is in fair agreement with the turbulent boundary-layer results.","url":"cran.html#doc125","title":"Measurements of skin friction of the compressible turbulent boundary layer on a cone with foreign gas injection."},
{"description":"Batchelor, G.K. Quart. J. Mech. App. Math. Vol. Vii, /2/, 1954, P. 179-192. The frictional force on a cylinder moving steadily parallel to its length through a viscous liquid which is initially at rest is determined with reasonable accuracy over the whole range of values of the duration of the motion and for a wide variety of shapes of the cylinder cross-section. When the time t is small, the first approximation gives a force per unit area which is the same as that for a flat plate of infinite width. The second approximation takes the shape of the cylinder into account and the force on unit length of cylinder is determined in terms of the number of corners, and their angles, in the cylinder cross linder is the same, to this approximation, as that on a circular cylinder of the same perimeter. For large values of t the determination of the frictional force is reducible to that of a potential problem, the solution of which is known for a number of different shapes. The approximations for small and large values of t for any one cylinder do not overlap but can be joined without much ambiguity. For no value of t do the forces on cylinders of different shape /excluding those whose curvature is not everywhere inwards/ differ by more than about 25 per cent.","title":"The skin friction on infinite cylinders moving parallell to their length.","url":"cran.html#doc786"},
{"description":"Ehret, D.M. Naca tn.2250, 1950. The hypersonic similarity law as derived by tsien has been investigated by comparing the pressure distributions along bodies of revolution at zero angle of attack. In making these comparisons, particular attention was given to determining the limits of mach number and fineness ratio for which the similarity law applies. For the purpose of this investigation, pressure distributions determined by the method of characteristics for ogive cylinders for values of mach numbers and fineness ratios varying from 1.5 to 12 were compared. Pressures on various cones and on cone cylinders were also compared in this study. The pressure distributions presented demonstrate that the hypersonic similarity law is applicable over a wider range of values of mach numbers and fineness ratios than might be expected from the assumptions made in the derivation. This is significant since within the range of applicability of the law a single pressure distribution exists for all similarly shaped bodies for which the ratio of free-stream mach number to fineness ratio is constant. Charts are presented for rapid determination of pressure distributions over ogive cylinders for any combination of mach number and fineness ratio within defined limits.","url":"cran.html#doc56","title":"An analysis of the applicability of the hypersonic similarity law to the study of the flow about bodies of revolution at zero angle of attack."},
{"title":"An experimental and theoretical investigation of second-order supersonic wing-body interference, for a non-lifting body with wings at incidence.","url":"cran.html#doc1075","description":"Wilby, P.G. Aero. Res. Inst. Of sweden, ffa report 87, 1960. Pressure distributions on the wing of two wing-body combinations are measured experimentally at mach numbers 3 and 4 with the wing at various incidences in the range 0degree to 10degree. The results are compared with theoretical results which include interference effects calculated according to the second-order supersonic wing-body interference theory due to landahl and beane /1/. This theory, having been tested previously for non-lifting wing-body combinations, is thus tested also for wings at incidence. The agreement between theory and experiment is found to vary with mach number and wing sweepback. For the higher mach number and moderate sweepback the theory gives a good prediction of pressure distribution, but for the most adverse condition of low mach number and large sweepback the theory is found to overestimate the interference effects. This is expected as the theory assumes the sweepback of the wings is small compared with that of the mach line. An empirical guide to the limit of application of the interference theory is given. Within this limit the agreement between theory and experiment is found to deteriorate only a little with increase of incidence, over the range tested."},
{"title":"Shock wave and flow field development in hypersonic re-entry.","url":"cran.html#doc1391","description":"Probstein, R.F. Ars. J. 31, 185-194, 1961. A study is made of when and how a shock wave and continuum-type flow field develop in the nose region of a highly cooled blunt body re- entering the atmosphere at hypersonic speed and in a free molecular flow regime. The various types of flow regimes encountered down to low altitude conditions are delineated, and the nature of the flow field and behavior of some of the aerodynamic characteristics are discussed. It is shown that for a highly cooled body, free molecule flow conditions occur at a higher altitude than previously indicated. Based on available evidence, it is suggested that kinetic theory solutions, which are essentially modified free molecule results, along with the navier-stokes equations with no surface slip, serve to define all of the flow regimes except for a narrow transitional layer regime which has a height of less than one factor of 10 in free stream density change. It is also suggested that the appearance of a definable shock wave occurs very rapidly in terms of density change near the beginning of the transitional layer regime, and that its location, as in continuum flow, is governed principally by the body geometry, whereas its thickness is determined by a local mean free path."},
{"description":"Clarke, J.F. Coa R.149, 1961. A heat conduction problem is set up which, in essence, simulates the conditions arising when a plane shock wave reflects from a co-planar solid boundary. The gas is assumed to be polyatomic, with one the quantity of primary interest is the temperature of the solid at the interface, since this can be observed experimentally without much difficulty. Solutions are obtained for this quantity which cover a range of practically plausible relaxation times and 'wall effect' parameters. It is essential to include proper temperature jump boundary conditions for both active and relaxing (or inert) energy modes. Thus it is necessary to know accommodation coefficients for these modes of energy storage. The temperature jump effects are found to dominate the (interface) solid's temperature time history, with relaxation effects playing a very secondary role. The theoretical results are compared with some experimental observations and encouraging agreement is found. As a result of this agreement it proves possible to estimate the accommodation coefficient for the active modes (in this case for the combination platinum air), the pressure being about 15 atmospheres. The pressure sensitivity of accommodation effects is commented on.","title":"Heat conduction through a polyatomic gas.","url":"cran.html#doc518"},
{"title":"A wind-tunnel test technique for measuring the dynamic rotary stability derivatives at subsonic and supersonic speeds.","url":"cran.html#doc790","description":"Report 1258 Benjamin H. Beam A method is described for measuring the dynamic stability derivatives of a model airplane in a wind tunnel. The characteristic features of this system are that single-degree-of-freedom oscillations were used to obtain combinations of rolling, yawing and pitching motions., that the oscillations were excited and controlled by velocity feedback which permitted operation under conditions unfavorable for more conventional types of oscillatory testing., and that data processing was greatly simplified by using analog computer elements in the strain-gage circuitry. The system described is primarily for measurement of the damping derivatives damping in roll damping in pitch, damping in yaw, and the cross derivatives rolling moment due to yawing and yawing moment due to rolling. The method of testing also permits measurement under oscillatory conditions of the static derivatives rolling moment due to sideslip, yawing moment due to sideslip, and pitching moment due to angle of attack. All these derivatives are of particular importance in estimating the short-period oscillatory motions of a rigid airplane. A small number of experimental data are included to illustrate the general scope of results obtainable with this system."},
{"description":"Forbes dewey, C. A.I.A.A. J. 1963, 20. The problem of predicting the characteristics of a hypersonic laminar boundary layer that interacts with the external flow field is approached using the tangent wedge formulation for the inviscid flow field and the method of similar solutions for the viscous flow. It is shown that the concept of local similarity which allows the pressure gradient parameter to vary in the streamwise direction leads to an explicit relation between the viscous and inviscid flows for all values of the hypersonic interaction parameter. The conditions of /strong/ and limits of the general relations. The present theory is compared with three independent experimental investigations. In each case, the agreement is found to be excellent over the range of investigated. It is shown, using asymptotic solutions to the exact boundary layer equations, that the present theory is applicable to a wide variety of viscous interaction problems. A large number of solutions to the laminar boundary layer similarity equations for a perfect gas with cross flow and surface mass transfer are given. These numerical results, when combined with the solutions of previous authors, are sufficient to describe the range of conditions with high precision.","title":"Use of local similarity concepts in hypersonic viscous interaction problems.","url":"cran.html#doc540"},
{"description":"Murphy, J.S. J.aero.scs. 20, 1953, 338. The laminar flow of a viscous incompressible fluid over a two-dimensional curved surface is investigated for two cases, one in which the curvature is /large/ and the other in which it is cases are obtained as approximations from the exact equations of motion by an order-of-magnitude analysis. These equations are solved for flow over a particular surface with zero surface pressure gradient. In this analysis, the pressure gradient normal to the surface is included, and the outer boundary conditions are modified in accordance with the requirements of flow over a curved surface. The results indicate that for equal reynolds numbers, the stress on convex surfaces is less than the flat-plate value, while the stress on concave surfaces is greater than for a flat plate. The most important effect of surface curvature, for the cases considered, is the modification of the shape of the velocity profile near the /outer edge/ of the boundary layer. The requirement that a smooth transition exist between the viscous flow and the potential flow at the outer edge of the layer causes the profile to have a negative slope near the outer edge for convex surface curvature and a positive slope for concave surface curvature.","title":"Some effects of surface curvature on laminar boundary layer flow.","url":"cran.html#doc133"},
{"description":"Leggett, D.M.A. Arc r + M.1991, 1941. Reasons for investigation.--for an efficient design of spar with thin sheet web it is important to know the load which will just cause the web to buckle. As stiffeners divide the web into panels, it is required to find the buckling stress of rectangular panels bounded on two sides by spar flanges and on the other two sides by stiffeners. Boundary conditions which represent closely this type of edge fixing are clamping (along the flanges) and simple support critical shear stress for a square panel held in this way. Conclusions and further development.--it is found that the value of the critical shear stress is almost midway between its values when all four edges are clamped and all four edges are simply supported. The method of solution developed in this report is of very general application, and can be used to investigate the stability of rectangular panels when the loading is any combination of shear and compression or tension, and the edges are clamped or simply supported, and not necessarily all clamped or all simply supported. By an easy extension the method of solution can also be used to find the periods of transverse vibration of rectangular panels for the same types of loading and edge fixing.","title":"The buckling of a square panel under shear, when one pair of opposite edges is clamped and the other pair is simply supported.","url":"cran.html#doc1387"},
{"url":"cran.html#doc1157","title":"Hypersonic shock tunnel.","description":"Nagamatsu, H.T. Et al. Ars J.V. 29, may 1959, pp 332-340. A hypersonic shock tunnel has been developed for obtaining fluid mechanic information at the high mach numbers and corresponding stagnation temperatures encountered in flight by long range ballistic vehicles and satellites. This report describes the hypersonic shock tunnel and presents some of the results obtained in the driven tube and in the nozzle helium is ignited in the driver to produce strong shock waves in air. A shock velocity in air as high as 55, 000 fps with a calculated equilibrium temperature of 16, 000 k has been produced in the driven tube. The effects of high stagnation temperatures upon the detached shock wave and the pressure distribution for blunt bodies have been observed in the nozzle test section. The detachment distance devreased greatly at high temperatures. The pressure distribution for the hemisphere was found to be less than that predicted by the modified newtonian theory. Shock wave boundary layer interaction at the leading edge of a flat plate was observed, and the results agreed with the analytical prediction. A detached shock wave was observed for a blunt two-dimensional body at very low densities in the test section with a flow mach number of 19.6."},
{"url":"cran.html#doc801","title":"Experimental study of the equivalence of transonic flow about slender cone-cylinders of circular and elliptic cross section.","description":"Page, W.A. Naca tn.4233, 1958. This report describes an experimental investigation of the equivalence relationship and the related theory for lifting forces proposed by transonic slender-body theory. The models chosen for this study are a flat, winglike, elliptic cone-cylinder and its equivalent body of revolution, a circular cone-cylinder. It is determined that the flows about the two models are closely related in the manner predicted by the theory, the relationship persisting over a mach number range of 0.92 to cone-cylinder vary linearly only over the small angle-of-attack range of approximately 1 and that the aerodynamic loading at sonic speed compares favorably with jones' slender-wing theory. The results of the investigation suggest that at transonic speeds and at small angles of attack the calculation of all aerodynamic characteristics of slender, three-dimensional shapes can be made by use of transonic slender-body theory when the pressures on the equivalent body of revolution are known, either by experiment, or by an adequate nonlinear theory. From transonic slender-body theory it is deduced that the slenderness required for this application is the same as that required for the successful application of the transonic area rule."},
{"description":"Low, G.M. Nasa r-3, 1959. Simplified expressions describing the transfer from a satellite orbit to the point of atmospheric entry are derived. The expressions are limited to altitude changes that are small compared with the earth's radius, and velocity changes small compared with satellite velocity. They are further restricted to motion about a spherical, nonrotating earth. The transfer orbit resulting from the application of thrust in any direction at any point in an elliptic orbit is considered. Expressions for the errors in distance (miss distance) and entry angle due to an initial misalinement and magnitude error of the deflecting thrust are presented. The largest potential contributing factor towards a miss distance stems from the misalinement of the retrovelocity increment. If this velocity increment is pointed in direct opposition to the flight path, a 1 misalinement leads to a miss distance of 34.5 miles. However, it is shown that this error can be avoided by applying the velocity increment at an angle between 120 and 150 below the flight-path direction. The guidance and accuracy requirements to establish a circular orbit, in addition to the corrections applied to transform elliptic orbits into circular ones, are also discussed.","title":"Nearly circular transfer trajectories for descending satellites.","url":"cran.html#doc162"},
{"url":"cran.html#doc734","title":"The bending of uniformly loaded clamped plate in the form of a circular sector.","description":"Hasse, H.R. Q. J. Mech. App. Math. 3, 1950, 271. The deflexion of a uniformly loaded plate in the form of a semicircle clamped along its boundary is obtained by a method due to weinstein. This problem requires the solution of the biharmonic equation where z is given, subject to the conditions that w = 0 and on the boundary, n being the direction of the outward normal. The solution is expressed in the form where, writing is found by solving (in succession) two harmonic equations of the forms where z may be zero, and where f and have to satisfy certain boundary conditions. The constants are then determined to satisfy the boundary condition. Numerical calculations show that five or six terms of the series give a good approximation to the accurate value as judged by the closeness with which the approximate solution satisfies the boundary condition. The procedure to be adopted in the case of the general circular sector and for non-uniform loading is indicated briefly. The connexion between the deflexion problem and that of plane strain in which the stress function satisfies the equation, where and have given values on the boundary, is discussed as a preliminary to the further consideration of the latter problem by a method of the same type."},
{"description":"Schubauer, G.B. And Skramstad, H.K. Naca r909, 1948. This is an account of an investigation in which oscillations were discovered in the laminar boundary layer along a flat plate. These oscillations were found during the course of an experiment in which transition from laminar to turbulent flow was being studied on the plate as the turbulence in the wind stream was being reduced to unusually low values by means of damping screens. The first part of the paper deals with experimental methods and apparatus, measurements of turbulence and sound, and studies of transition. A description is then given of the manner in which oscillations were discovered and how they were found to be related to transition, and then how controlled oscillations were produced and studied in detail. The oscillations are shown to be the velocity variations accompanying a wave motion in the boundary layer, this wave motion having all the characteristics predicted by a stability theory based on the exponential growth of small disturbances. A review of this theory is given. The work is thus experimental confirmation of a mathematical theory of stability which had been in the process of development for a period of approximately 40 years, mainly by german investigators.","url":"cran.html#doc207","title":"Laminar boundary layer oscillations and transition on a flat plate."},
{"description":"Keenan, J.H. Asme trans. 1949, 773. A machine for testing turbine nozzles by the reaction method, which was described in a previous paper, was used to test a series of convergent-divergent turbine nozzles. The results of these tests, along with the test of a convergent turbine nozzle, are compared with each other and with analytical values. Two kinds of analytical values are employed, namely, the usual values obtained from an assumed isentropic expansion from inlet state to exhaust pressure, and the values obtained from the assumption that the processes in the nozzle are isentropic except for a normal shock which takes up a position in the nozzle such as to cause the stream to fill the exit area at the exhaust pressure whenever possible. This latter kind of analytical value involves no shock when the exit area can be filled at the exhaust pressure by means of isentropic processes only, or when the exhaust pressure is lowered so far that the shock has passed out of the passage. The agreement of the test results with the calculated results of this latter kind is good, and the disagreement which exists can be attributed largely to separation at the shock and to transmission of exhaust-pressure effects upstream through the boundary layer.","title":"Reaction tests of turbine nozzles for supersonic velocities.","url":"cran.html#doc276"},
{"description":"Leggett, D.M.A. And Jones, R.P.N. Arc r + M.2190, 1942. The value of the compressive stress at which a thin circular cylindrical shell becomes unstable has been worked out theoretically by southwell (1914). Subsequent experimental results, however, have indicated that this value is appreciably too high and that the form of distortion which occurs in practice differs from that assumed in theory. In recent years much work has been done on this problem in america. Lundquist (1933) and donnell (1934) have concluded that the buckling of a cylindrical shell is greatly influenced by initial irregularities,. Von karman and tsien (1941) have indicated that a thin cylindrical shell can be maintained in a buckled state by a compressive load considerably smaller than that previously predicted by theory. The present paper is an extension of the work of von karman and tsien. It shows that the smallest load which will keep a thin cylindrical shell in a buckled condition is about one-third of that given by southwell, a result in very fair agreement with experiment, and that once the cylinder has buckled, and so long as the stresses remain within the elastic range of the material, the cylinder has only about one-quarter of its original stiffness.","title":"The behaviour of a cylindrical shell under axial compression when the buckling load has been exceeded.","url":"cran.html#doc740"},
{"url":"cran.html#doc51","title":"Theory of aircraft structural models subjected to aerodynamic heating and external loads.","description":"O'sullivan, W.J. Naca tn.4115, 1957. The problem of investigating the simultaneous effects of transient aerodynamic heating and external loads on aircraft structures for the purpose of determining the ability of the structure to withstand flight to supersonic speeds is studied. By dimensional analyses it is shown that.. Constructed of the same materials as the aircraft will be thermally similar to the aircraft with respect to the flow of heat through the structure will be similar to those of the aircraft when the structural model is constructed at the same temperature as the aircraft. External loads will be similar to those of the aircraft. Subjected to heating and cooling that correctly simulate the aerodynamic heating of the aircraft, except with respect to angular velocities and angular accelerations, without requiring determination of the heat flux at each point on the surface and its variation with time. Acting on the aerodynamically heated structural model to those acting on the aircraft is determined for the case of zero angular velocity and zero angular acceleration, so that the structural model may be subjected to the external loads required for simultaneous simulation of stresses and deformations due to external loads."},
{"description":"Cohen, C.B. And Reshotko, E. Naca R.1294, 1956. An approximate method for the calculation of the compressible laminar boundary layer with heat transfer and arbitrary pressure gradient, based on thwaites' correlation concept, is presented. The method results from the application of stewartson's transformation to prandtl's equations, which yeilds a nonlinear set of two first-order differential equations. These equations are then expressed in terms of dimensionless parameters related to the wall shear, the surface heat transfer, and the transformed free-stream velocity. Thwaites' concept of the unique interdependence of these parameters is assumed. The evaluation of these quantities is then carried out by utilizing exact solutions recently obtained. With the resulting relations, methods are derived for the calculation of the two-dimensional and axially symmetric laminar boundary layer with arbitrary free-stream velocity distribution. Mach number, and surface temperature level. The combined effect of heat transfer and pressure gradient is demonstrated by applying the method to calculate the characteristics of the boundary layer on thin supersonic surfaces and in a highly cooled, convergent-divergent, axially symmetric rocket nozzle.","title":"The compressible laminar boundary layer with heat transfer and arbitrary pressure gradient.","url":"cran.html#doc1366"},
{"description":"Bloom, M.G. And Steiger, M.H. J. Aero. Sc. V. 27, pp 821-835, 1960. One-dimensional inviscid nonequilibrium flows of a two-component model gas are studied for prescribed pressure variations and an average reaction rate based on recent data for oxygen recombination. These flows are interpreted in relation to the flow along streamlines around blunt hypersonic bodies. Assuming equilibrium conditions in the subsonic region, it is estimated that the flow in the initial supersonic expansion region, which is approximately of prandtl-meyer character, will be chemically frozen with respect to the molecular dissociation of the primary components under the hypersonic, high-altitude flight conditions considered. The flight conditions consist of flight velocities between furthermore, on bodies of small surface inclination beyond the nose, the flow will continue to be effectively frozen for at least 20 ft down-stream of the nose. These conclusions may lead to the simplification of procedures for theoretical calculation and testing. The problem of distinguishing a dimensionless length-reaction rate parameter, which characterizes the extent of departures from equilibrium or from frozen behavior in the flow fields of interest here, is discussed","title":"Inviscid flow with nonequilibrium molecular dissociation for pressure distributions encountered in hypersonic flight.","url":"cran.html#doc574"},
{"title":"Stability of cylindrical and conical shells of circular cross section, with simultaneous action of axial compression and external normal pressure.","url":"cran.html#doc934","description":"Mushtari, K.M. And Sachenkov, A.V. Naca tm.1433, 1958. We consider in this report the determination of the upper limit of critical loads in the case of simultaneous action of a compressive force, uniformly distributed over plane cross sections, and of isotropic external normal pressure on cylindrical or conical shells of circular cross section. As a starting point we use the differential equations for neutral equilibrium of conical shells (ref. 1) which have been used for the solution of the problem of stability of conical shells under torsion and under axial compression (ref. 2),. Upon solution of the problem it is possible to satisfy all boundary conditions, in contrast to the report (ref. 3) where no attention is paid to the fulfillment of the boundary conditions and to the report (ref. 4) where only part of the boundary conditions are satisfied by solution of the problem according to galerkin's method. Approximate formulas are used for the determination of the critical external normal pressure with simultaneous action of longitudinal compression. Let us note that the formulas suggested in reference 5 are not well founded and may lead, in a number of cases, to a substantial mistake in the magnitude of the critical load."},
{"description":"Spreiter, J. R. And Alksne, A. Y. Naca tn 3970, may, 1957. The present paper describes a method for the approximate solution of the nonlinear equations of transonic small disturbance theory. Although the solutions are nonlinear, the analysis is sufficiently simple that results are obtained in closed analytic form for a large and significant class of nonlifting airfoils. Application to two-dimensional flows with free-stream mach number near 1 leads, for instance, to general expressions for the determination of the pressure distribution on an airfoil of specified geometry and for the shape of an airfoil having a prescribed pressure distribution and gives, furthermore, the correct variation of pressure with mach number at mach number 1. For flows that are subsonic everywhere, the method yields a pressure-correction formula that is more accurate than the prandtl-glauert rule and compares favorably with existing higher approximations. For flows that are supersonic everywhere, the method yields the equivalent, in transonic approximation, of simple wave theory. Results obtained by application of these general expressions are shown to correspond closely to existing solutions and to experimental data for a wide variety of airfoils.","url":"cran.html#doc467","title":"Thin airfoil theory based on approximate solution of the transonic flow equation."},
{"url":"cran.html#doc1302","title":"The development of the boundary layer in supersonic shear flow.","description":"Rogers, R.H. Rae tn.aero.2738, 1961. The development of the boundary layer in a velocity shear layer is discussed for two-dimensional flow and for axisymmetric flow of both compressible and incompressible fluids. It is shown that the solutions obtained by li and glauert for the two-dimensional flow of an incompressible fluid are applicable in the more general case after suitable transformations of coordinates have been made. New definitions are shown to be necessary, and are given, for the displacement and momentum thicknesses of such a boundary layer. Reynolds numbers based on these thicknesses are given, and it is shown that any phenomenon which occurs at a constant value of such a reynolds number will occur at a point which, as the length scale of the flow increases, first moves down-stream and then moves slightly upstream. This is shown to be in qualitative agreement with experimental results on a blunt cone in a supersonic flow. A quantitative comparison of the theoretical and experimental values of displacement and momentum thicknesses is attempted, and no disagreement is obvious,. Unfortunately the accuracy of the experiments so far available is insufficient to give positive confirmation of the theory of this note."},
{"description":"Graham, E.W. J. Ae. Scs. 1958, 771. The problem studied may be regarded as a problem of geometry. Its simplest form (loosely stated) is then as follows.. A mountain rises up from the x-y plane. Determine the exact shape of the mountain knowing only the cross-sectional area of every possible cut which can be made through the mountain with a vertical plane. In a more complicated version of the problem, the given information might be restricted to the cross-sectional area of every cut which can be made by a vertical plane inclined less than 45 to the y-axis. This latter case has direct applications to certain minimum drag problems in supersonic flow. The shape of the mountain corresponds to the (unknown) shape of the optimum lift distribution on a planar wing. The cross-sectional area of a cut is the integrated value of the lift along a straight line crossing the wing plan form. For a restricted range of line inclinations, these optimum integrated lift values can sometimes be determined directly. Here it is assumed that they are given. The problem in its simplest form was originally solved by radon, who found solutions for a large class of such problems. The derivation presented here may perhaps be more readily understood.","title":"A geometric problem related to the optimum distribution of lift on a planar wing in supersonic flow.","url":"cran.html#doc561"},
{"description":"Murduchow, M. J. Ae. Scs. 19, 1952, 705. A simple expression is derived for the normal injection velocity distribution theoretically required to maintain a given uniform temperature along a porous surface in the laminar boundary-layer region of a compressible flow with a given velocity distribution outside of the boundary layer. This expression is valid for any given free-stream mach number but is based on a prandtl number of unity and on the assumption that the viscosity coefficient varies linearly with the temperature. By using the dorodnitsyn type of transformation, the variation of fluid properties even in the case of zero mach number is taken into account. This study is of particular practical interest in connection with the sweat-cooling of turbine blades and of airfoil surfaces in high speed flow. The method of analysis consists of applying the karman-pohlhausen method to both the momentum and energy boundary-layer equations and of using an additional heat balance equation, involving the coolant temperature. A closed-form approximate solution of the equations is then derived. Numerical examples for flow in the immediate vicinity of a stagnation point and for a typical type of flow over a turbine blade are given.","title":"On heat transfer over a sweat-cooled surface in laminar compressible flow with a pressure gradient.","url":"cran.html#doc352"},
{"url":"cran.html#doc1214","title":"The drag of elongated bodies over a wide reynolds number range.","description":"Robertson, J.M. And Clark, M.E. J. Ae. Scs. 1962, 842. The resistance of bodies in motion through an incompressible viscous fluid is predictable from stokes- or oseen-type solutions in the creeping-motion range, while some test information is available in the boundary-layer range. With the exception of experimental results for spheres or circular cylinders and analytical and experimental results for flat plates, almost no information is available on other bodies, particularly in the intermediate range of reynolds numbers extending from unity to a million. Experimental results as obtained from hydroballistic studies in water and glycerin-water solutions are presented for finned ellipsoids of fineness-ratio.4 over a 20, 000-fold range and are correlated with available information on other bodies. Although results do not extend down to the creeping-motion region where analytical predictions are available, comparison with the drag coefficient trends for spheres and flat plates indicates that an appropriate curve for the ellipsoid could be extended so as to cover the entire laminar-viscous range. Less extensive results are presented on the drag of fineness-ratio 8 ellipsoids and on laminar-turbulent transition occurrences."},
{"title":"Scale height in the upper atmosphere, derived from changes in satellite orbits.","url":"cran.html#doc622","description":"King-hele, D.G. And Hughes, K.M. R.A.E. Tn space 4, 1962. The'density scale height'h in the upper atmosphere is a measure of the rate at which air density p varies with height y, being given by h-p//dp/dy/. The value of h, although important because/with the molecular weight of the air/it determines the air temperature, has not as yet been well determined at heights above 200 km. This note develops methods for finding h from the decrease in a satellite's perigee height and from the decrease in the orbital period of a satellite in a small-eccentricity orbit. These methods are then applied to all the 14 satellites found suitable for the purpose. The 44 values of h obtained, for heights of 200-450 km, represent an average over day and night and probably have errors/S.D./of 5-10(. It is found that, as solar activity declined between 1957 and 1961, h decreased greatly..E.G.at height 275 km, h decreased from 60 km in early 1958 to height becomes much less rapid above 350 km, and are consistent with the supposition that h had low values, near 35 km, at heights near 250 km, for 1959-61. The results could be greatly extended in scope and improved in accuracy if more accurate orbits were available for short-lifetime satellites."},
{"description":"Biot, M.A. J. Ae. Scs. 1962, 558. Boundary-layer heat transfer is analyzed for the case of a sinusoidal distribution of temperature in the direction of flow. It is shown that for both laminar and turbulent flow the spatial distribution of heat transfer is generally out of phase with the wall temperature by an angle of 30 to 45. This leads to the conclusion that in some areas the heat flow is opposite to the temperature difference as used in the definition of the heat-transfer coefficient, and points to the basic shortcomings of this concept. The physical explanation for this behavior is found to be the temperature-field distortion by the fluid motion. The distortion is measured by the peclet number. Approximate equations representing a /conduction analogy/ were used in this analysis and the validity of these equations for unsteady flow is examined with reference to limitations in frequency and wavelength. A solution of these equations is given for the case of a velocity profile which is not a straight line. The use of previously developed variational principles for the evaluation of convective heat transfer including cases of three-dimensional unsteady flow, turbulence, and nonparallel streamlines is also discussed.","title":"Fundamentals of boundary layer heat transfer with streamwise temperature variations.","url":"cran.html#doc872"},
{"description":"Nielsen, J.N., kaattari, G.E. And Anastasio, R.F. Naca til.3959. A method is presented for calculating the lift and pitching-moment characteristics of circular cylindrical bodies in combination with triangular, rectangular, or trapezoidal wings or tails through the subsonic, transonic, and supersonic speed ranges. The method covers unbanked wings, sweptback leading edges or sweptforward trailing edges, low angles of attack, and the effects of wing and tail incidence. The wing-body interference is handled by the method presented in naca rm's a51j04 and a52b06, and the wing-tail interference is treated by assuming one completely rolled-up vortex per wing panel and evaluating the tail load by strip theory. A computing table and set of design charts are presented which reduce the calculations to routine operations. Comparison is made between the estimated and experimental characteristics for a large number of wing-body and wing-body-tail combinations. Generally speaking, the lifts were estimated to within 10 percent and the centers of pressure were estimated to within effect of wing deflection on wing-tail interference at supersonic speeds was not correctly predicted for triangular wings with supersonic leading edges.","title":"A method for calculating the lift and centre of pressure of wing-body-tail combinations at subsonic, transonic speeds.","url":"cran.html#doc924"},
{"title":"The buckling of sandwich type panels.","url":"cran.html#doc1127","description":"Hoff, N.H. And Mautner, S.F. J. Ae. Scs. 1945, 285. Fifty-one flat rectangular sandwich-type panels were tested in edgewise compression with the unloaded edges of the panels restrained by v-grooves. The sandwich consisted of papreg faces and a cellular cellulose acetate core. The thickness of the faces varied from 0.00675 to 0.02025 in.,. The core, from 0.066 to 0.741 in.,. The width of the panel, from 4 to 11 in. The length of the panel was always 10.5 in. The buckled shape consisted of a ripple of short wave length across the panel. It was either symmetric, the two faces bulging out symmetrically according to sine curves, or skew, the two faces deflecting in the same sense according to sine curves having a phase angle of 90. A strain energy theory of buckling is presented for both the symmetric and the skew cases, and the buckling load in the symmetric case is also calculated by integration of the differential equation. The agreement between the theoretic and the experimental buckling stress is reasonable, that between the predicted and actual buckled shape good. A simple formula is developed which permits a choice of the most suitable core material when the mechanical properties of the face material are given."},
{"description":"Ostrach, S. J. Ae. Scs. 29, 1962, 289. The problem of determining the stability of compressible viscous flows with nonzero surface velocities is formulated and is shown to be identical to that for conventional boundary layers, with only a redefinition of the mach and reynolds numbers required. Specific consideration is given to the wall boundary layer behind a moving shock wave, and the minimum critical reynolds numbers are obtained for various shock velocities. The entire stability map is determined for the limiting case of a weak wave, which is analogous to the rayleigh problem. The minimum critical reynolds number is found to increase monotonically with shock velocity--I.E., with increasing surface cooling and stream mach number combined. For the ratio of wall to stream velocity of 2.92 with (shock mach number of 2.18) the flow is found to be infinitely stable to two-dimensional disturbances. Experimental transition data do not follow the trends predicted by the theory. In fact, the transition reynolds numbers are orders of magnitude below the computed minimum critical reynolds numbers. The lack of correlation between theory and experiment is attributed to disturbances which are external to the boundary layer.","title":"Stability of compressible boundary layers induced by a moving wave.","url":"cran.html#doc504"},
{"description":"Inger, G.R. A.I.A.A. J. 1963, 46. This paper is concerned with the similitude laws governing inviscid, nonequilibrium gas flows around blunt or sharp-nosed slender bodies at zero angle of attack, based on the hypersonic small disturbance flow theory. Some related features of the interaction between the effects of nose bluntness and nonequilibrium dissociation and vibration and the influence of a dissociated freestream are also discussed. The hypersonic equivalence principle and the related similitude for affinely related bodies are set forth for nonequilibrium flows in either diatomic gases or a gas mixture such as air. For a family of diatomic gases, as opposed to a given gas such as air, a generalized ambient gas state scaling condition is obtained, whereby the ambient density and temperature need not be simulated. A detailed discussion is given of blunted cylinders and slabs or sharp-nosed cones and wedges, including example nonequilibrium flow field correlations of numerical solutions available in the literature. Low density nonequilibrium flows with a negligible shock layer atom recombination rate are also examined ,. As expected, a less restrictive small disturbance similitude law is obtained in this case.","url":"cran.html#doc541","title":"Similitude of hypersonic flows over slender bodies in non-equilibrium dissociated gases."},
{"description":"Wu, J.M., chapkis, R.L. And Mager, A. Ars journal, 1677-1685, 1961. A study has been made of the side force generated by injection of secondary material into the main stream of a rocket nozzle. Two cases have been analyzed.. Gas injection and liquid injection. For the gas injection case, it is assumed that the turbulent boundary layer ahead of the injection point separates from the wall. The pressure in the separated region and the extent of the separated region are determined by a consideration of turbulent boundary layer-shock wave interaction and the accommodation height of the injected gas stream. Equations are derived for calculating the side force, and the side forces predicted by the theory are compared with experimental data. The agreement between theory and experiment is fair. For the case of liquid injection, it is assumed that the liquid flows along the nozzle wall and evaporates into the main stream. The resulting side force on the nozzle wall is determined on the basis of linearized theory, thus restricting the analysis to small rates of liquid injection. The effects of small rates of heat addition are also included in the analysis. A very simple equation for calculating the side force is obtained.","url":"cran.html#doc974","title":"Approximate analysis of thrust vector control by fluid injection."},
{"description":"Biot, M.A. J.ae.scs.26, 1959. Lagrangian methods in heat-flow problems and transport phenomena were introduced by the writer in some previous work. The present paper develops further one particular aspect of the method, --I.E., the elimination of /ignorable coordinates./ this is accomplished by a special choice of generalized coordinates, each of which is constituted by an arbitrary temperature distribution and an /associated flow field./ the latter is a vector field which is derived from the corresponding scalar field by a variational method. The procedure is valid for a certain class of nonlinear problems, provided we replace the temperature by the heat content as the unknown. It is shown that for normal coordinates derivation of the associated flow field is immediate. The use of normal coordinates and their associated flow fields is illustrated by an example. Introduction of dirac functions and associated flow fields yields a procedure which constitutes a generalization of the classical formulation by green's functions and integral equations. This is illustrated by application to one-dimensional problems of heating of a homogeneous or composite slab and directly verified by classical methods in the appendix.","title":"Further developments of new methods in heat flow analysis.","url":"cran.html#doc579"},
{"url":"cran.html#doc255","title":"An approximate solution of the turbulent boundary layer equations in incompressible and compressible.","description":"Lilley, G.M. Coa r134, 1960. If over the 'outer region' of the boundary layer, where the mean velocity varies but little from its value outside the shear layer, a virtual eddy viscosity is defined, which is constant over the outer region but varies in the direction of the mainstream, a solution of the turbulent boundary layer equations can be found which satisfies the appropriate boundary conditions. The solution leads to a compatibility condition for the virtual eddy viscosity in terms of the wall shear stress, the boundary layer momentum thickness and the mainstream velocity, at least for the case of a constant external velocity. This compatibility condition, which can be expressed as for moderate to high reynolds numbers, where is the shear velocity, is the boundary layer thickness and is the virtual eddy (kinematic) viscosity, is just the condition townsend (1956) found for the equilibrium of the large eddies. The numerical value of the constant derived by townsend agrees with ours for reynolds numbers (based on x) of about. With this relation for an equation, analoguous to the momentum integral equation solution, can be found for as a function of local freestream velocity, with one disposable parameter."},
{"title":"Theoretical pressure distribution on a hemisphere-cylinder combination.","url":"cran.html#doc370","description":"Anthony casaccio Research assistant, aerodynamics laboratory, polytechnic institute of brooklyn, freeport, N.Y. In recent years great use has been made of approximate methods for the determination of the pressure distribution on blunt-nosed bodies and afterbodies at high mach numbers. For quasi-spherical bodies it has been suggested that modified newtonian theory in combination with a prandtl-meyer expansion be used on the nose portion, the two laws being matched at the point where the pressure gradients are equal. No simple approximation, however, has been found for flat-nosed bodies. As for the pressure distribution on the afterbody, the blast-wave analogy has been suggested for general nose shapes but particular afterbody profiles. The purpose of the present note is to compare these approximate estimates with a more accurate determination of the flow field about a hemisphere-cylinder in an ideal gas flow. It was felt that since experimental investigations in air at this mach number are scarce and very difficult to obtain, the comparison would be of interest. The basis of comparison is the flow field as it results from a numerical integration of the exact equations governing the motion of the ideal fluid."},
{"description":"Kramer, J.J. Et al. Nasa tn d-1186, 1962. The nonviscous flow through a mixed-flow pump impeller having one splitter vane between adjacent main blades has been analyzed on a blade-to-blade surface of revolution using a previously reported analysis method. Solutions were obtained for a variety of flow conditions including several cases in which whirl is imparted to the flow upstream of the impeller. The velocity distributions on the main-blade surfaces and on the splitter-vane surfaces in the region of the splitter vane were strongly dependent on the assumed location of the rear stagnation points. Solutions were obtained by assuming values of slip factor and of division of flow around the splitter in addition to assuming the location of the rear stagnation points. These solutions indicated that the velocity distributions in the splitter-vane region are largely determined by the division of flow around the splitter vane and that only the region in the immediate vicinity of the trailing edge is affected by the slip factor. Blade surface velocities were obtained from two approximate methods by specifying flow division and slip factor, and these results are compared with the more exact solutions of the analysis.","title":"Incompressible nonviscous blade-to-blade flow through a pump rotor with splitter vanes.","url":"cran.html#doc989"},
{"title":"Use of freon-12 as a fluid for aerodynamic testing.","url":"cran.html#doc1335","description":"Huber, P.W. Naca tn.1024, 1946. The thermodynamic properties of freon-12 have been investigated to determine the possibilities of the use of this gas as a fluid for aerodynamic testing. The values of velocity of sound in freon-12, which are less than one-half those in air, are presented as functions of temperatures and pressure, including measurements at room temperature. The density of freon-12 is about four times that of air. Changes in state of freon-12 may be predicted by means of the ideal gas law with an accuracy of better than 1 percent at pressures below freon-12 is shown not to condense during an adiabatic expansion from normal conditions up to a mach number of 3. The values of the ratio of specific heats for freon-12 are lower than that for air, and therefore an additional parameter is introduced, which must be considered when comparisons are made of aerodynamic tests using freon-12 with those using air. The time lag of the vibrational heat capacity of freon-12 to a change in temperature has been measured and found to be of the order of 2 x 10 second at atmospheric temperature and pressure. This time is so short that no important energy dissipations should result in most engineering applications."},
{"title":"A theory for the core of a leading edge vortex.","url":"cran.html#doc191","description":"Hall, M.G. Rae R.aero.2644, 1960. In the flow past a slender delta wing at incidence can be observed a roughly axially symmetric core of spiralling fluid, formed by the rolling up of the shear layer that separates from a leading edge. The aim in this report is to predict the flow field within this vortex core, given appropriate conditions at its outside edge. The basic assumptions are core. In addition it is assumed that the flow is axially symmetric and incompressible. Together, these admit outer and inner solutions for the core from the equations of motion. For the outer solution the sub-core is ignored, and the flow is taken to be inviscid (but rotational) and conical. The resulting solution consists of simple expressions for the velocity components and pressure. For the inner solution, which applies to the diffusive sub-core, the flow is taken to be laminar, and approximations, some based on the boundary conditions and some analogous to those of boundary layer theory, are made. The solution obtained in this case is a first approximation, and is presented in tabular form. A sample calculation yields results which are in good qualitative and fair quantitative agreement with experimental measurements."},
{"description":"Katzen, E.D. And Levy, L.L. Nasa tn.d1145, 1961. 5. An analysis has been made of atmosphere entries for which the vehicle lift-drag ratio was modulated to maintain specified maximum decelerations and or maximum deceleration rates. The part of the vehicle drag polar used during modulation was from maximum lift coefficient to minimum drag coefficient. The entries were at parabolic velocity and the vehicle maximum lift-drag ratio was 0.5. Two-dimensional trajectory calculations were made for a nonrotating, spherical earth with an exponential atmosphere. The results of the analysis indicate that for a given initial flight-path angle, modulation generally resulted in a reduction of the maximum deceleration to 60 percent of the unmodulated value or a reduction of maximum deceleration rate to less than 50 percent of the unmodulated rate. These results were equivalent, for a maximum deceleration of 10g, to lowering the undershoot boundary 24 miles with a resulting decrease in total convective heating to the stagnation point of 22 percent. However, the maximum convective heating rate was increased 18 percent,. The maximum radiative heating rate and total radiative heating were each increased about 10 percent.","title":"Atmospheric entries with vehicle lift-drag ratio modulated to limit deceleration and rate of deceleration vehicles with maximum lift-drag ratio of 0. 5.","url":"cran.html#doc1344"},
{"title":"Random vibration.","url":"cran.html#doc908","description":"Crandal, S. App. Mech. Rev. 12, 1959, 739. Random vibration is vibration which results from an excitation which is not well represented by any simple function (sinusoid, step, etc.) or any simple combination of such functions but which is satisfactorily modeled by a stochastic process. It is perhaps not too much of an exaggeration to say that /all vibration is random vibration./ every vibration record contains /hash/ at some level. Nevertheless, until recently, engineering vibration theory has been able to get along without including the consideration of random excitations. Now in several fields simultaneously there has occurred a burst of activity in the application of random processes. The response of aircraft to buffeting from atmospheric turbulence and the response of ships to confused seas have been put on reasonably firm footing. Possibly the most dramatic problems have been posed by the development of large jet and rocket engines which produce spectacular amounts of random vibrational energy. The high level of random vibration in a jet plane or a missile provides a severe environment with respect to fatigue failure of structural members and with respect to malfunctions of sensitive equipment."},
{"url":"cran.html#doc1216","title":"Pressure distribution in regions of step-induced turbulent separation.","description":"Vasilu, J. J. Ae. Scs. 1962, 596. An analysis is made of the pressure distribution in the separated-flow region ahead of a step, using the concept of the turbulent mixing coefficient of crocco and lees and the /jet-flow/ model of chapman with some modification. On the basis of a variable mixing coefficient, a differential equation for the pressure distribution is derived, which gives the pressure rise as a function of the distance from the separation point. This equation contains the separation length as an unknown. A second equation is obtained by making a mass balance of the air entering and, leaving the /dead-air/ region ahead of the step. The pressure rise and the separation distance for a given mach number are determined by solving the two equations simultaneously. The analysis yields results which are in close agreement with the experimental data on steps, obtained at princeton, particularly for m = 3.85. For lower mach numbers, a maximum variation of 5 percent is found between theory and experiment. Use of the velocity profiles of jets, as required by the jet-flow model, necessarily restricts the applicability of the present study to flows with thin boundary layers at the separation point."},
{"title":"Constant-temperature magneto-gasdynamic channel flow.","url":"cran.html#doc34","description":"Kerrebrock, J.P. And Marble, F.E. J. Ae. Scs. 27, 1960, 78. In the course of investigating boundary-layer flow in continuous plasma accelerators with crossed electric and magnetic fields, it was found advantageous to have at hand simple closed-form solutions for the magneto-gasdynamic flow in the duct which could serve as free-stream conditions for the boundary layers. Nontrivial solutions of this sort are not available at present, and in fact, as in the work of resler and sears, the variation of conditions along the flow axis must be obtained through numerical integration. Consequently, some simple solutions of magneto-gasdynamic channel flow were sought, possessing sufficient algebraic simplicity to serve as free-stream boundary conditions for analytic investigations of the boundary layer in a physically reasonable accelerator. In particular, since the cooling of the accelerator tube is likely to be an important physical problem because of the high gas temperatures required to provide sufficient gaseous conductivity, channel flow with constant temperature appears interesting. Some simple algebraic solutions for the case of a constant temperature plasma are developed in the following paragraphs."},
{"description":"Nash, W.A. J.app.mech. 1952, 33. Three methods of approximating the deflections and moments occurring in a rectangular cantilever plate subjected to uniform normal pressure over its entire surface are presented in this paper. The first is the application of the well-known finite-difference procedure. The second and third are collocation methods, one based upon polynomial solutions of the lagrange equation, the other employing /mixed/ hyperbolic-trigonometric terms satisfying this equation. In the last two methods the boundary conditions are satisfied exactly along the clamped edge and at a finite number of points along the free edges of the plate. The results obtained for the particular case of a cantilever plate with uniform normal load indicate that the use of a relatively small number of points in the collocation method yields values of deflections and moments that are in substantial agreement with those given by the finite-difference procedure. It cannot be concluded from these results that the collocation method using the assumed functions will give satisfactory results with fewer points than the finite-difference method for cantilever plates with loading different from the one investigated.","title":"Several approximate analyses of the bending of a rectangular cantilever plate by uniform normal pressure.","url":"cran.html#doc454"},
{"description":"Drischler J.A. Naca tn 3639, 1956. The unsteady-lift functions for a wing undergoing a sudden change in sinking speed have been presented for delta wings having aspect ratios of 0, 2, and 4 and for rectangular and elliptical wings having aspect ratios of 0, 3, and 6. For the elliptical and rectangular wings the spanwise lift distributions were also presented. These functions were calculated from the lift coefficients associated with a wing oscillating harmonically in pure translational motion, as obtained from several sources. The results of these calculations indicate that the normalized unsteady-lift functions are substantially independent of the shape of the plan form for elliptical, rectangular, or moderately tapered wings,. However, for delta wings the increase of lift toward the steady-state value is much more rapid than that for the aforementioned wings of the same aspect ratio. These results also corroborate the results of other investigations in that the rate of growth of lift tends to increase with a decrease in aspect ratio. The shape of the spanwise distributions of the indicial lift seems to be, for all practical purposes, independent of time for rectangular and elliptical wings.","url":"cran.html#doc699","title":"Approximate indical lift functions for several wings of finite span in incompressible flow as obtained from oscillatory lift coefficients."},
{"url":"cran.html#doc1398","title":"Stability of rectangular plates under shear and bending forces.","description":"Way, S. J. App. Mech. 3, 1936, a131. The author first discusses the problem of a plane, simply supported rectangular plate loaded by shearing forces in the plane of the plate on all four edges. There are two stiffeners attached one third and two thirds of the way along the plate. The critical load is calculated for various stiffener rigidities. Also, the rigidity necessary to keep the stiffeners straight when the plate buckles is found. This stiffener rigidity is found to be slightly larger than that necessary for a plate with one stiffener and the same panel dimensions as the plate with two stiffeners. The second problem discussed by the author is that of a plane, simply supported rectangular plate loaded by uniformly distributed edge shearing forces in the plane of the plate and linearly distributed tension and compression in the plane of the plate at the ends. The end forces vary from tension, at one corner to, at the other corner, so that their resultant is a bending moment. The presence of the edge shearing forces is found to diminish the critical bending stress in this case. Calculations are made for various magnitudes of bending and shearing forces for plates of various proportions."},
{"description":"Ting-yili Department of aeronautical engineering, rensselaer polytechnic institute troy, N.Y. In the study of high-speed viscous flow past a two-dimensional body it is usually necessary to consider a curved shock wave emitting from the nose or leading edge of the body. Consequently, there exists an inviscid rotational flow region between the shock wave and the boundary layer. Such a situation arises, for instance, in the study of the hypersonic viscous flow past a flat plate. The situation is somewhat different from prandtl's classical boundary-layer problem. In prandtl's original problem the inviscid free stream outside the boundary layer is irrotational while in a hypersonic boundary-layer problem the inviscid free stream must be considered as rotational. The possible effects of vorticity have been recently discussed by ferri and libby. In the present paper, the simple shear flow past a flat plate in a fluid of small viscosity is investigated. It can be shown that this problem can again be treated by the boundary-layer approximation, the only novel feature being that the free stream has a constant vorticity. The discussion here is restricted to two-dimensional incompressible steady flow.","title":"Simple shear flow past a flat plate in an incompressible fluid of small viscosity.","url":"cran.html#doc2"},
{"description":"Carrier, G.F. J. App. Mech. 11, 1944, 134. The problem of evaluating the bending moments, existing in a uniformly loaded clamped plate having the form of a sector of a ring, is one which arises in connection with the stress analysis of reinforced piston heads and in other design problems. In this paper, expressions are derived for the bending moments along the edges of such a plate. Similar problems, I.E., those of the clamped rectangular plate under uniform pressure, under a central concentrated load, and that of the simply supported sector of a disk under uniform pressure, have been discussed by previous authors. The general approach used in the foregoing problems is adopted in the present case ,. A considerable reduction in the computational work is achieved, however, by the use of an integral-equation method of solving the boundary-condition equations. Numerical results are obtained for plates of various dimensions, and the edge moment distributions are plotted for these cases. Curves are also plotted which indicate the relationship existing between the maximum bending moments derived for sectorial plates and those previously obtained for clamped rectangular plates of similar size.","url":"cran.html#doc733","title":"The bending of a sectorial plate."},
{"url":"cran.html#doc1024","title":"Note on creep buckling of columns.","description":"The general dynamic equation of creep bending of a beam loaded laterally and axially was derived for a linearly viscoelastic material whose mechanical properties can be characterized by four parameters. The material can exhibit instantaneous and retarded elasticity as well as pure flow. The equation derived was used to obtain the creep bending deflection of a beam in pure bending and of a column with initial sinusoidal deviation from straightness. As expected, the ratio of the creep deflections of the beam in pure bending and the deflections of a corresponding purely elastic structure is identical to the ratio of the creep strain and the corresponding elastic strain of a bar under simple tension or compression. The results of the analysis of the creep deflection of the column showed that the deflections increase continuously with time and become infinitely large only when the loading time is correspondingly large. However, large deflections are obtained in reasonably short periods of time if the applied load is near to the euler load of the column. The deflection-time curves obtained from a numerical example are of the same type as those determined by experiment with aluminum columns."},
{"title":"Nonlinear deflections of shallow spherical shells.","url":"cran.html#doc830","description":"Reiss, E.L., greenberg, H.J. And Keller, H.B. J. Ae. Scs. 24, 1957, 533. The equations obtained by chien for the nonlinear deflection of shallow spherical shells under uniform external pressure are solved by means of power series expansions, following procedures introduced by friedrichs and stoker in their treatment of buckling of circular plates. These equations depend upon two parameters. One of these parameters is related to the external pressure, while the other depends upon the dimensions of the shell. The equations are solved for several ranges of the parameters under boundary conditions corresponding to a fixed edge. The solution, carried out numerically on the aec univac at new york university, yields a complete description of the stresses and deflections as functions of the polar angle over a wide range of values of the loading parameter and the dimensional parameter. Prediction of the upper buckling load is then made by means of a numerical criterion based on the load vs. Deflection curve. For some cases, the postbuckling behavior is investigated. The results agree well with existing experimental and theoretical studies and cover a wide range of cases not previously treated."},
{"url":"cran.html#doc222","title":"The flow over delta wings at low speeds with leading edge separation.","description":"Marsden, D.J., simpson, R.W. And Rainbird, W.J. Coa r114, 1957. A low speed investigation of the flow over a 40 apex angle delta wing with sharp leading edges has been made in order to ascertain details of the flow in the viscous region near the leading edge of the suction surface of the wing. A physical picture of the flow was obtained from the surface flow and a smoke technique of flow visualization, combined with detailed measurements of total head, dynamic pressure, flow directions and vortex core positions in the flow above the wing. Surface pressure distributions were also measured and integrated to give normal force coefficients. The results of this investigation were compared with those of other experimental investigations and also with various theoretical results. In particular, the normal force coefficients, vortex core positions and attachment line positions were compared with the theoretical results of mangler and smith, reference 19. It was found that.. Exist on the upper surface of the wing outboard of and below the main vortices. These secondary vortices are formed as a result of separation of the boundary layers developing outboard of the top surface attachment lines."},
{"description":"Owen, P.R. And Anderson, R.G. Rae R.aero.2471, 1952. The interference between the wings and the tail surfaces of a combination of circular body, low aspect ratio cruciform wings and cruciform tail in an inviscid flow is analysed using the slender body theory. The system may be subjected to both incidence and yaw and, in general, the tail fins may be staggered angularly with respect to the main wings. The method is a development of that used by owen and maskell in R.A.E. Report no. Aero.2441 to analyse similar effects on a system set at zero yaw. Simple expressions to determine the strengths and positions of the trailing vortices (supposed to be rolled-up) downstream of the main wings are given, and from them the forces on the tail are deduced. When the tail surfaces are triangular and of low aspect ratio an exact solution is obtained from slender body theory.. But for rectangular tail surfaces of moderate or high aspect ratio, it is suggested that the changes in lift and sideforce on the tail caused by the wing vortex field can be estimated approximately from the mean upwash and sidewash angles evaluated over the respective tail spans. Formulae for these means angles are presented.","title":"Interference between the wings and tail surfaces of a combination of slender body, cruciform wings and cruciform tail set at both incidence and yaw.","url":"cran.html#doc229"},
{"description":"Jones, G.W. And Dubose, H.C. Naca rml53g10a, 1953. An investigation of the effects of systematic variations in wing plan form on the flutter speed at mach numbers between 0.73 and 1.43 has been conducted in the 26-inch langley transonic blowdown tunnel. The angle of sweepback was varied from 0degree to 60degree on wings of aspect ratio 4, and the aspect ratio was varied from 2 to 6 on wings with experimental flutter speed and the reference flutter speed calculated on the basis of incompressible two-dimensional flow. This ratio, designated as the flutter-speed ratio, is plotted as a function of mach number for the various wings. It is found that the flutter-speed ratio increased rapidly past sonic speed for sweep angles of 45degree and less, indicating a favorable effect of mach number. For sweepback of mach number range of the tests. Reducing the aspect ratio had a favorable effect on the flutter-speed ratio which was of the order of 100 percent higher for the aspect-ratio-2 wing than for the aspect-ratio-6 wing. This percentage difference was nearly constant throughout the mach number range, indicating that the effect of mach number was about the same for all aspect ratios tested.","title":"Investigation of wing flutter at transonic speeds for six systematically varied wing plan forms.","url":"cran.html#doc1341"},
{"description":"Southwell, R.V. Q. J. Mech. App. Math. 3, 1950, 257. The displacement of a flat plate bent by transverse loading, and the extensional or in 'plane stress', are governed by equations of identical form ,. And The boundary conditions have identical form when edge-displacements are specified in the flexural, edge-tractions in the extensional problem, so mathematically, in these circumstances, only a single problem is presented. This, the 'first analogue' relating flexure and extension, is well known. A 'second analogue', relating the flexural problem when edge-tractions with the extensional problem when edge-displacements are specified, is believed to have been first propounded in 1941. By introducing two quantities u and v, analogous with the components u and v of extensional displacement, it permits a treatment of the flexural problem by any method--E.G. Which yields extensional solutions of this second type. In this paper both analogues are combined in an inclusive statement covering the perforated (multiply connected) plates which were discussed in 1948. Reasons are stated for believing that 'two-diagram technique' is preferable in problems governed by 'mixed' boundary conditions.","title":"On the analogues relating flexure and extension of flat plates.","url":"cran.html#doc732"},
{"description":"Hills, P.R. Naca report 1372, 1958. A method of calculating the temperature of thick walls has been developed in which are used relatively new concepts, such as the time series and the response to a unit triangle variation of surface temperature, together with essentially standard formulas for transient temperature and heat flow into thick walls. The method can be used without knowledge of the mathematical tools of its development. The method is particularly suitable for determining the wall temperature in one-dimensional thermal problems in aeronautics where there is a continuous variation of the heat-transfer coefficient and adiabatic-wall temperature. The method also offers a convenient means for solving the inverse problem of determining the heat-flow history when temperature history is known. A series of diversified problems were solved by exact analysis as well as by the new method. A comparison of the results shows the new method to be accurate. The labor involved is very modest in consideration of the nature of the thick-wall temperature problem. Limiting solutions for the /infinitely thick/ wall and for walls so thin that thermal lag can be neglected were also obtained.","title":"A method of computing the transient temperature of thick walls from arbitrary variation of adiabatic-wall temperature and heat-transfer coefficient.","url":"cran.html#doc980"},
{"description":"Van dyke, M.D. Naca r1183, 1954. A solution to second order in thickness is derived for harmonically oscillating two-dimensional airfoils in supersonic flow. For slow oscillations of an arbitrary profile, the result is found as a series including the third power of frequency. For arbitrary frequencies, the method of solution for any specific profile is indicated, and the explicit solution derived for a single wedge. Nonlinear thickness effects are found generally to reduce the torsional damping, and so to enlarge the range of mach numbers within which torsional instability is possible. This destabilizing effect varies only slightly with frequency in the range involved in dynamic stability analysis, but may reverse to a stabilizing effect at high flutter frequencies. Comparison with a previous solution exact in thickness suggests that nonlinear effects of higher than second order are practically negligible. The analysis utilizes a smoothing technique that replaces the actural problem by one involving no kinked streamlines. This stratagem eliminates all consideration of shock waves from the analysis, yet yields the correct solution for problems that actually contain shock waves.","url":"cran.html#doc201","title":"Supersonic flow past oscillating airfoils including nonlinear thickness effects."},
{"url":"cran.html#doc1114","title":"Steady and fluctuating pressures at transonic speeds on two space-vehicle payload shapes.","description":"Coe, C.F. Nasa tm.x503, 1961. Steady and fluctuating pressures have been measured at mach numbers which were varied from 0.6 to 1.2 on two bodies of revolution typical of two space-vehicle payload shapes, the centaur and the able V. The results of the investigation showed that significant fluctuations of pressure occurred on both bodies between mach numbers of 0.75 and 1.00. The maximum fluctuations measured at any mach number and angle of attack occurred in the region of the normal shock wave as a result of shock-wave motion. Large regions of unsteady pressure also occurred as a result of separation on the converging afterbody of the able-v model. The maximum pressure fluctuations occurring on the bodies increased with increasing angle of attack. For angles other than are indicated since pressure fluctuations were larger on the upper half of the bodies than on the lower half. No definite conclusions could be drawn regarding the form of the spectral densities of pressure fluctuations in the region of the shock wave. The spectral densities in regions of separation following the shock wave appeared flat except for some increase in energy level below due to slight model motions."},
{"description":"Yashura, M. J.phys.soc. Japan, 11, 1956, 878. A similar solution of the hypersonic viscous flow past slender bodies of revolution is deduced for a special case when the radial coordinate of the body surface at section x is proportional to x, where the radial coordinate have the comparable order value with the thickness of the boundary layer. Here, /similar/ is used in the direct meaning that distributions in the boundary layer keep the similar form lengthwise. Calculations are accomplished for the region of strong interaction between the boundary layer and the shock wave. From several calculations it may be expected that if the thickness of the body becomes small, the thickness of the layer in which the longitudinal velocity component u is rapidly decreased also becomes small, and in the major part of the boundary layer, only the normal component v is increased. Further if the thickness of the body is increased, then, the height of the shock wave, the pressure on the wall, and the shear stress at the wall are also increased while the boundary layer thickness is decreased. The nose region is excluded by the reason that the ordinary boundary layer theory will be invalid there.","url":"cran.html#doc192","title":"On the hypersonic viscous flow past slender bodies of revolution."},
{"title":"Free-flight measurements of the static and dynamic stability and drag of a 10 blunted cone at mach numbers 3.5 and 8.5.","url":"cran.html#doc1000","description":"Intrieri, P. F. Nasa tn. D1299, 1962. 5 and 8.5. Tests were made of a short blunt-nosed without a 50 half-angle conical afterbody in a pressurized ballistic range at nominal mach numbers of 3.5 and of 90, 000 and 220, 000, respectively. It was found that the models were statically stable about the center- of-gravity location tested but exhibited neutral dynamic stability for flight at constant altitude. The static stability was not affected by the but was nonlinear with angle of attack and varied with mach number. The nonlinear variation of the pitching moment with angle of attack was accurately approximated by a cubic polynomial. The static stability was only qualitatively predicted by modified newtonian theory. The drag characteristics were in good agreement with values calculated by use of modified newtonian theory. Calculations of the oscillatory behavior of the configurations flying an example entry trajectory through the martian atmosphere indicated the configurations to be dynamically satisfactory. Pitching motions should converge to a small fraction of the amplitude at entry, provided the initial angle of attack and pitch rate are not large enough to cause tumbling."},
{"description":"Irving weinstein National aeronautics and space administration. Technical note d-1503 An experimental investigation has been made to indicate the validity of using methane-air combustion products as the test medium for aerodynamic heating and loading tests. Tests were conducted on a hemisphere-cylinder and on a bluff-afterbody model, both in methane-air combustion products and in air alone, and covered a range of mach numbers from 6 to the data showed that the nondimensional heating-rate distribution along a hemisphere-cylinder as obtained in combustion products was in good agreement with that obtained in air, and the results were in reasonable agreement with theory. The stagnation-point heating rates in air and in combustion products over the hemisphere-cylinder agreed within 10 percent of the theoretical values. The pressure distributions around a hemisphere-cylinder obtained from tests in combution products were in good agreement with those obtained in air and could be predicted by newtonian flow theory. The tests in combustion products of a bluff-afterbody model produced nondimensional heat-transfer coefficients which were in fair agreement with results obtained in air.","title":"Heat transfer and pressure distributions on a hemisphere-cylinder and a bluff-afterbody model in methane-air combustion products and in air.","url":"cran.html#doc635"},
{"description":"The phenomenological theory previously proposed in naca technical note 4000 for the behavior of metals at elevated temperatures has been modified to yield transient creep curves by assuming that the metal consists of two phases, each with its own elasticity and viscosity. The extended theory satisfies the basic requirements for a theory of transient creep at elevated temperatures.. That the transient creep be closely connected with the subsequent steady creep, and that the apparent exponent of the time in the transient region be permitted wide variations between 0 and 1. From this theory it is possible to construct nondimensional creep curves which extend continuously from the transient region into the steady-state region. The corresponding family of creep curves for any metal may be obtained from the nondimensional family by use of appropriate constants. The constants required are those obtained from steady creep measurements, together with two additional constants which represent the difference between the phases. The transient creep curves resulting from this theory are compared with the experimental curves for pure aluminum, gamma iron, lead, and agreement is found.","url":"cran.html#doc1028","title":"Note on creep buckling of columns."},
{"description":"Larson, H.K. J. Ae. Scs. 1959, 731. Results of an experimental heat-transfer investigation in regions of separated flow are presented and compared with the theoretical analysis of naca tn 3792. The average heat transfer for both laminar and turbulent separated boundary layers was found to be from 35 to 50 per cent less than that for equivalent attached boundary layers. The overall scope of the measurements included mach numbers from 0.3 to 4.0 and reynolds numbers from 10 to 4 x 10. The results for laminar boundary layers agree well with the analysis of tn 3792. The results for turbulent boundary layers, however, disagree considerably. Results of velocity and temperature surveys in the separated turbulent boundary layer are presented and partially explain the discrepancy between the experiments and analysis. The maximum local heat-transfer rates were found to occur in the reattachment region of the separated boundary layers investigated. The effect of transition on heat transfer in the separated laminar boundary layers is described and data showing effects of mach number and wall temperature on the transition reynolds number of separated laminar flows are also included.","title":"Heat transfer in separated flows.","url":"cran.html#doc959"},
{"title":"Axisymmetric free mixing with swirl.","url":"cran.html#doc1371","description":"Steiger, M.H. And Bloom, M.H. Pibal R.628. Viscous laminar axially-symmetric free-mixing with small, moderate, and large swirl is investigated by a boundary layer type of analysis with integral methods. Moderate and small swirls are formally the same, differing only in the order of their associated radial pressure gradients. Neither induces significant axial pressure gradients,. Consequently their effect on the axial flow is negligible. For moderate and small swirl an interesting feature is the swirl decay. In both compressible and incompressible flow, it is shown that jet swirl decays more rapidly than wake swirl whereas both swirls decay more rapidly than the non-uniformity in axial velocity. Large swirl generates axial pressure gradients as well as large radial pressure gradients, and therefore alters the streamwise flow. Examples calculated for incompressible flow, show that the wake is lengthened by large swirl. It is expected that this effect will be diminished in the presence of higher free-stream mach numbers which lead to decreased densities, due to decreased centrifugal effects, decreased radial pressure gradients, and decreased axial pressure gradients."},
{"url":"cran.html#doc997","title":"Experimental and theoretical studies of axisymmetric free jets.","description":"Love, E.S. Et al. Nasa tr r-6, 1959. Some experimental and theoretical studies have been made of axisymmetric free jets exhausting from sonic and supersonic nozzles into still air and into supersonic streams with a view toward problems associated with propulsive jets and the investigation of these problems. For jets exhausting into still air, consideration is given to the effects of jet mach number, nozzle divergence angle, and jet static-pressure ratio upon jet structure, jet wavelength, and the shape and curvature of the jet boundary. Studies of the effects of the ratio of specific heats of the jets are included as are observations pertaining to jet noise and jet simulation. For jets exhausting into supersonic streams, an attempt has been made to present primarily theoretical curves of the type that may be useful in evaluating certain jet interference effects and in formulating experimental studies. The primary variables considered are jet mach number, free-stream mach number, jet static-pressure ratio, ratio of specific heats of the jet, nozzle exit angle, and boattail angle. The simulation problem and the case of a hypothetical hypersonic vehicle are examined"},
{"description":"Treon, S.L. Nasa tn.d1327, 1962. 6 to 5. 5 and angles of attack to 180. Wind-tunnel tests have been performed at mach numbers from 0.6 to 5.5 to determine coefficients of normal force, axial force, and pitching moment for short blunt cones, as affected by changes in nose and base cone angles. Models with nose half-angles of 10 and 20 were investigated. The 10 nose half-angle models were tested with a flat base and with base cones of 50 and 70 half-angle. The 20 nose half-angle model had a 50 half-angle base cone. Reynolds numbers for the test ranged from about maximum diameter. Variations in the base cone angle resulted in significant changes in the aerodynamic characteristics, with lesser effects resulting from changes in nose cone angle. In particular, the model with the 50 half-angle conical base had only one trim angle flat base and 70 half-angle conical base had two trim angles (a = 0 and a = 180). Estimated variations of the aerodynamic characteristics with angle of attack by means of a modified newtonian theory were in good agreement with the experimental results. The theory, however, failed to predict the trim point at a = 180 for the flat-based model.","title":"Static aerodynamic characteristics of short blunt cones with various nose and base cone angles at mach numbers of 0. 6 to 5. 5 and angles of attack to 180.","url":"cran.html#doc999"},
{"url":"cran.html#doc135","title":"The calculation of wall shearing stress from heat-transfer measurements in compressible flows.","description":"Nick S. Diaconis Lewis flight propulsion laboratory, naca, cleveland, ohio It has been shown by ludwieg that the wall shearing stress of a laminar or turbulent boundary layer in an incompressible flow can be determined from a heat-transfer measurement at the surface. The instrument used in that investigation was essentially a small, locally insulated, heating element embedded in the test surface. The size of the instrument was restricted by the condition that the thermal boundary layer generated by the heating element be contained locally within the laminar sublayer. In the present analysis ludweig's theory for such an instrument is extended to compressible flow over an insulated flat plate. With the same limitations on the design and operation of the instrument as mentioned above, it can also be assumed for compressible laminar and turbulent boundary layers that only the flow in the immediate vicinity of the wall or the laminar sublayer will be affected in the region of the heated element. This assumption then permits the use of the laminar boundary-layer equations as the governing equations for this analysis for both laminar and turbulent boundary layers."},
{"title":"Nonsimilar solutions of the compressible laminar boundary layer equations with applications to the upstream-transpiration cooling problem.","url":"cran.html#doc1240","description":"Pallone, A. J. Ae. Scs. 1961, 449. A new method is presented for predicting the boundary-layer characteristics downstream of the porous region of an injection-cooled surface. The method consists of a general scheme for obtaining nonsimilar solutions of the compressible- laminar-boundary-layer equations and is formulated along the following lines. The viscous domain is divided into n curvilinear strips. The governing equations are then integrated along the coordinate normal to the body from the surface to the boundary of each strip. As a result, one obtains a set of independent integro-differential relations. The integration is carried out by expressing the integrands as polynomials, the coefficients of which are functions of the unknown values of the velocity and temperature on the strip boundaries as well as of the imposed boundary condition at the wall and at the outer edge. After the integration is performed, a set of ordinary first-order differential equations is obtained. The set of equations may be solved for given initial conditions by a numerical integration scheme such as the runge-kutta method. Several numerical examples of interest are presented."},
{"description":"Coltrane, L.C. Nasa tn.d1506, 1962. 30 to 2. 85. A cone with a blunt nose tip and a blunt nose tip and a 20 flared cylinder afterbody have been tested in free flight over a mach number range from 0.30 to 2.85 and a reynolds number range from 1 x 10 to 23 x 10. Time histories, cross plots of force and moment coefficients, and plots of the longitudinal-force coefficient, rolling velocity, aerodynamic center, normal-force-curve slope, and dynamic stability are presented. With the center-of-gravity location at about models were both statically and dynamically stable throughout the mach number range. For the cone, the average aerodynamic center moved slightly forward with decreasing speeds and the normal-force-curve slope was fairly constant throughout the speed range. For the ogive, the average aerodynamic center remained practically constant and the normal-force-curve slope remained practically constant to a mach number of approximately 1.6 where a rising trend was noted. Maximum drag coefficient for the cone, with reference to the base area, was approximately 0.6, and for the ogive, with reference to the area of the cylindrical portion, was approximately 2.1.","title":"Stability investigation of a blunted cone and a blunted ogive with a flared cylinder afterbody at mach numbers from 0. 30 to 2. 85.","url":"cran.html#doc759"},
{"title":"A study of the acoustic fatigue characteristics of some flat and curved aluminium panels exposed to random and discrete noise.","url":"cran.html#doc727","description":"Hess, R.W., herr, R.W. And Mayes, W.H. Nasa tn.d1. A study was made of the fatigue life of simple 2024-t3 aluminum-alloy panels measuring 11 by 13 inches and exposed to both discrete-frequency noise from a siren and random noise from an air jet. Noise levels varied from approximately panel variables included thickness, edge conditions, curvature, and static-pressure differential. No significant differences were noted in the nature of failures experienced for the two types of loadings. At a given root-mean-square stress level, the failure times were generally shorter for the random loading than for the discrete-frequency loading. These differences in failure times were noted to be a function of stress level, the larger differences occurring at the lower stress levels. Increases in time to failure were obtained as a result of increased panel thickness, increased panel curvature, and particularly for increased static-pressure differential across curved panels. For the discrete-type loading, the location of weak points in these simplified structural designs can be satisfactorily accomplished but quantitative predictions of fatigue life are much more difficult."},
{"title":"Investigation of the jet effects on a flat surface downstream of the exit of a simulated turbojet nacelle at a free-stream mach number of 2.02.","url":"cran.html#doc692","description":"Bressette, W.E. Naca rm l54e05a, 1954. 02. An investigation at a free-stream mach number of 2.02 was made to determine the effects of a propulsive jet on a wing surface located in the vicinity of a choked convergent nozzle. Static-pressure surveys were made on a flat surface that was located in the vicinity of the propulsive jet. The nozzle was operated over a range of exit pressure ratios at different fixed vertical distances from the flat surface. Within the scope of this investigation, it was found that shock waves, formed in the external flow because of the presence of the propulsive jet, impinged on the flat surface and greatly altered the pressure distribution. An integration of this pressure distribution, with the location of the propulsive jet exit varied from 1.450 propulsive-jet exit diameters to 3.392 propulsive-jet exit diameters below the wing, resulted in an incremental lift for all jet locations that was equal to the gross thrust at an exit pressure ratio of 2.86. This incremental lift increased with increase in exit pressure ratio, but not so rapidly as the thrust increased, and was approximately constant at any given exit pressure ratio."},
{"description":"Stewartson, K. J. Ae. Scs. 1961, 1. A study is made of the motion of an incompressible viscous fluid past a quarter-infinite plate, whose leading edge is perpendicular to and whose side edge is parallel to the undisturbed direction of the stream. It is assumed that the kinematic viscosity is small. The first approximation is taken to be the undisturbed motion, and successive approximations are obtained by iferation. The second approximation is the blasius shear layer necessary to satisfy the boundary conditions on the plate. In turn, this layer leads to a velocity component normal to the plate which needs a potential solution, in which the velocities are 0, to match with the conditions at infinity. Further, the match at the edge of the blasius shear layer must be completed to 0 by introducing a secondary shear layer. The regions near the leading and side edges are considered separately,. In particular, the neighborhood of the side edge needs special care, because the determination of the chief terms is complicated by the presence of powers of log. In particular it is shown that the effect of the edge is to change the skin-friction coefficient by a factor","title":"Viscous flow past a quarter infinite plate.","url":"cran.html#doc1251"},
{"description":"Maglieri, D.J. And Carlson, H.W. Nasa memo 3-4-59l, 1959. Data are presented which provide an insight into the nature of the shock-wave noise problem, the significant variables involved, and the manner in which airplane operation may be affected. Flight-test data are also given, and a comparison with the available theory is made. An attempt is also made to correlate the subjective reactions of observers and some associated physical phenomena with the pressure amplitudes during full-scale flight. It is indicated that for the proposed supersonic transport airplanes of the future, booms on the ground will most probably be experienced during the major portion of the flight plan. The boom pressures will be most severe during the climb and descent phases of the flight plan. During the cruise phase of the flight, the boom pressures are of much lesser intensity but are spread laterally for many miles. The manner in which the airplane is operated appears to be significant,. For example, the boom pressures during the climb, cruise, and descent phases can be minimized by operating the airplane at its maximum altitude consistent with its performance capabilities.","title":"The shock wave noise problem of supersonic aircraft in steady flight.","url":"cran.html#doc810"},
{"url":"cran.html#doc1088","title":"Iterative methods for solving partial difference equations of elliptic type.","description":"Young, D. Trans. Amer. Math. Soc. Vol. 76, P. 92, 1954. This paper considers linear systems /1/ where a includes matrices of a sort frequently occurring in the solution of elliptic partial differential equations by difference methods /in particular, a o/. Rewriting superscript is number of iteration cycle/ are used to compute u when u are used. Also, one may /over-relax/.. Ser. A. 210, 307-357 /1910/ who suggested changing from time to time to speed up convergence. In the present paper over-relaxation /with fixed w/ is combined with immediate introduction of newly-computed u's, a la gauss-seidel. Various theorems on convergence are proved$. In particular, it is shown that there exists an ordering of the equations and an optimum value wb such that in general /3/ converges much more rapidly than the gauss-seidel method /w 1/. Means are suggested for estimating wb,. The sensitivity of the rate of convergence to the choice of w is studied. The paper concludes with a theoretical comparison of gauss-seidel and the method proposed, /successive over-relaxation/, for solving dirichlet's difference problem over a square using a high-speed computing machine."},
{"title":"Base pressure in supersonic flow.","url":"cran.html#doc186","description":"Gadd, G.E., holder, D.W. And Regan, J.D. Arc cp271, 1956. The problem of accurately predicting the pressure and wake configuration at the base of bodies in supersonic flow is an extremely important one inasmuch as a sizeable portion of the total drag of a given body may be attributable to the low pressure in this region. Although a great deal of theoretical and experimental work has been done in this field, there does not yet exist a satisfactory method for accurate predictions. This paper represents an excellent effort to experimentally confirm analytically deduced concepts. A large amount of experimental data on body shapes such as wedges, cones, and cone-cylinders has been obtained over a range of mach numbers up to 4. The data are thoroughly discussed with respect to analytical deductions. On the basis of the evidence accumulated it is concluded that the boundary-layer thickness has only a small effect on the base pressure for axisymmetric bodies and for two-dimensional bodies when the base height-to-chord ratios are of the order. Reviewer believes this report is a significant contribution in the field of base pressure and wake flow phenomena."},
{"url":"cran.html#doc593","title":"Theoretical considerations of flutter at high mach number.","description":"Morgan, H.G., runyam, H.L. And Huckell, V. J. Ae. Scs. 25, 1958. Some of the theories for two-dimensional oscillatory air forces which may be applied in flutter calculations at high mach numbers are discussed. These include linear theory, van dyke's second-order theory, piston theory, landahl's method, tangent-wedge and tangent-cone approximations, newtonian theory, and a new nonlinear-pressure method. A comparison of the theories is made by showing the results of flutter calculations for mach numbers up to 10, and the possibility of flutter at these higher mach numbers is pointed out. Results of flutter calculations are shown to illustrate the various effects arising from a nonlinear thickness theory. The possibility of large flutter speed thickness effects which depend on frequency ratio is shown. The influence of airfoil shape is discussed and flutter speed trends with center of gravity and elastic axis locations are presented. Some possible refinements of piston theory are discussed for use at very high mach numbers. These include the use of local flow conditions and the use of newtonian theory over the leading edge of a blunt-nosed airfoil."},
{"url":"cran.html#doc283","title":"Laminar heat transfer around blunt bodies in dissociated air.","description":"Kemp, N.H., rose, P.H. And Detra, R.W. J.ae.sc. 26, 1959. A method of predicting laminar heat-transfer rates to blunt, highly cooled bodies with constant wall temperature in dissociated air flow is developed. Attention is restricted to the case of axisymmetric bodies at zero incidence, although two-dimensional bodies could be treated the same way. The method is based on the use of the /local similarity/ concept and an extension of the ideas used by fay and riddell. A simple formula is given for predicting the ratio of local heat-transfer rate to stagnation-point rate. It depends on wall conditions and pressure distribution, but not on the thermodynamic or transport properties of the hot external flow, except at the stagnation point. Experimental heat-transfer rates obtained with correct stagnation-point simulation and high wall cooling in shock tubes are also presented and compared with the theoretical predictions. On the whole, the agreement is good, although in regions of rapidly varying pressure there is evidence that the local similarity assumption breaks down, and the theory underestimates the actual heat-transfer rate by up to 25 per cent."},
{"description":"Vondoenhoff. Naca tn.3000, 1953. A number of studies relating to the use of freon-12 as a substitute medium for air in aerodynamic testing have been made. The use of freon-12 instead of air makes possible large savings in wind-tunnel drive power. Because of the fact that the ratio of specific heats is approximately 1.13 for freon-12 as compared with 1.4 for air, some differences exist between data obtained in freon-12 and in air. Methods for predicting aerodynamic characteristics of bodies in air from data obtained in freon-12, however, have been developed from the concept of similarity of the streamline pattern. These methods, derived from consideration of two-dimensional flows, provide substantial agreement in all cases for which comparative data are available. These data consist of measurements throughout a range of mach number from approximately 0.4 to 1.2 of pressure distributions and hinge moments on swept and unswept wings having aspect ratios ranging from 4.0 to 9.0, including cases where a substantial part of the wing was stalled. The freon charging and recovery system used for the langley low-turbulence pressure tunnel is described.","title":"Studies of the use of freon-12 as a wind tunnel testing medium.","url":"cran.html#doc1336"},
{"description":"Leissa, A.W. And Niedenfuhr, F.W. J. Aero. Sc. 29, 1962. Plate problems involving free edges have been historically difficult to solve, particularly when two free edges are adjacent, resulting in a free corner. The cantilevered square plate subjected to a transverse loading is one such problem for which an exact solution has not been achieved. In the present paper results obtained by various approximate methods are presented for this problem for the case of a uniform loading. Solutions obtained by the authors using the technique of point matching and the rayleigh-ritz method are compared with previously published finite-difference and experimental results and with bernoulli-euler beam and plane-strain approaches. Numerical results for deflections, slope components, bending and twisting moments, and transverse distributed shears are presented for a relatively fine gridwork of points on the plate boundary and within the interior. The antielastic curvature is exhibited by all methods except beam theory. All methods present the interesting conclusion that the free edge deflection is greater when the plate is treated as a plate rather than a beam.","title":"A study of the cantilever square plate subjected to a uniform loading.","url":"cran.html#doc644"},
{"url":"cran.html#doc414","title":"The problem of resistance in compressible fluids.","description":"Von karman, T. 5th volta cong. 1955, 226. This report is restricted to the resistance of bodies of revolution and of cylindrical bodies of infinite length moving with uniform velocity in a compressible fluid. In the case of bodies of revolution it will be assumed that the direction of the movement is parallel to the axis of symmetry. It will be assumed that the fluid satisfies the equation of state of perfect gases, I. E. Const., where p denotes the pressure, the density and t the absolute temperature. In addition to obeying this equation the fluid is characterized by the statement that the intrinsic energy of the unit mass amounts to where for simplicity's sake the specific heat will be expressed in work rather than heat units. The ratio between the specific heat at constant pressure and the specific heat at constant volume will be denoted by. It is known that the value of x depends upon the number of degrees of freedom of the molecules,. If this number is denoted by N. For air the value x = 1.4 will be used. The limiting case x = 1 will be referred to as that of a assumed that in the range considered and are independent of the temperature."},
{"url":"cran.html#doc1349","title":"Effects of simulated rocket jet exhaust on stability and control of a research type airplane configuration at a mach number of 6. 86.","description":"Fetterman, D.E. Nasa tm.x127, 1959. 86. An investigation has been undertaken in the langley 11-inch hypersonic tunnel at a free-stream mach number of 6.86 to determine the jet-interference effects at high jet-static-pressure ratios on the stability and control of a research-type airplane configuration. Compressed-air tests with a jet exhausting from the base of the fuselage were conducted over a reynolds number range of 0.57 x 10 to and over a jet-static- pressure-ratio range of 0 to 1460. The results of these tests indicated that the operation of the jet induced a sizable separated-flow region over the vertical- and horizontal-tail surfaces which could be approximately duplicated at low angles of attack by use of metal jet-boundary simulators. The results of force tests, during which these metal jet-boundary simulators were used, indicated that this separated-flow region caused a large reduction in the longitudinal stability and control and a smaller reduction in the lateral and directional stability and control. By extending the divergent section of the nozzle and thus reducing the jet-static-pressure ratio, these losses were diminished."},
{"description":"Lance, G.N. Aero. Quart. V. 6/2/, may, 1955. A generalised conical flow theory is used to deduce an integral equation relating the velocity potential on a delta wing/with subsonic leading edges/to the given downwash distribution over the wing. The complete solution of this integral equation is derived. This complete solution is composed of two parts, one being symmetric and the other antisymmetric with respect to the spanwise co-ordinate,. Each part represents a velocity potential. For example, if y is the spanwise co-ordinate and x is measured in the free stream direction, then a downwash of the form w-a ux/y/is symmetric and will give rise to a symmetric potential, whereas w-a ux/y/sgn y is anti-symmetric and gives rise to an anti-symmetric potential. The velocity potentials of such flows are given in the form of tables for all downwashes up to and including homogenous cubics in the spanwise and streamwise co-ordinates. Table iii gives similar formulae in the limiting case were used over a cycle of the tumbling motion. The analytical expression was in good agreement with numerical solutions of the complete non-linear equations of motion.","url":"cran.html#doc682","title":"The lift of twisted and cambered wings in supersonic flow."},
{"description":"A long, thin-walled cylindrical shell is loaded by a uniform external pressure. Equations are developed for the time behavior of the shape of the cross section under the following conditions.. Formations expressible by a power creep law,. (b) the initial and subsequent mode shape of the deviations from circularity of any cross section is two-lobed,. And (c) the shell construction is of the sandwich type, with concentric cylindrical membranes taking normal stresses and an annular core supporting shear without deformation. Explicit solutions are obtained for the particular case of the cubic creep law. It is shown that the nondimensional amplitude of the cross-sectional mode shape (briefly, shape factor) will become infinite in a finite time. Curves of shape factor versus time and of collapse time versus initial value of the shape factor are presented. Also given are an explicit expression for and a curve of the expected variation in collapse time owing to uncontrollable deviations from a nominal initial value of the shape factor. It is shown that the expected variation is small if the nominal initial shape factor value is sufficiently large.","title":"Note on creep buckling of columns.","url":"cran.html#doc1034"},
{"url":"cran.html#doc1294","title":"Non-linear shallow shell analysis by the matrix force method.","description":"Lansing, W., jones, I.W. And Ratner, P. Nasa tn.d1510, 1962, 753. The matrix force method of redundant structure analysis is currently being extended by various users to cover a number of non-linear problems. One of these is the non-linear analysis of heated cambered wings, such as might be used in advanced flight vehicles. In this case the approach used by the present authors is equally applicable to shallow shells, the formulation of the strain-displacement and equilibrium relations being a finite element equivalent to that used by marguerre. The solution is obtained by a combined iteration and step by step procedure utilizing a tangent flexibility matrix. Divergence in the calculations indicates that the range of stable configurations has been exceeded. Cambered plates subjected to several loadings are given as examples,. For one, an exact solution is available for comparison. It is believed that the basic concepts involved in this shallow shell analysis can be extended to apply to other, more general shell instability problems, and that useful solutions to the latter are probably within the capability of present day digital computers."},
{"description":"Drischler, J.A. Naca tn 3748, october 1956 The total lift responses of wings to sinusoidal gusts and to sinusoidal vertical oscillations are calculated from the response to gust penetration and to a sudden change in sinking velocity through use of the well-established reciprocal relations for unsteady flow. The cases considered are two-dimensional wings in incompressible, subsonic compressible, sonic, and supersonic flow,. Elliptical and rectangular wings in incompressible flow,. Wide rectangular and delta wings in supersonic flow,. And Delta wings of vanishingly low aspect ratio in incompressible and compressible flow. For most of the cases considered, closed-form expressions are given and the final results are presented in the form of plots of the square of the modulus of the lift coefficient for wings in a sinusoidally oscillating gust and in the form of the real and imaginary parts of the lift component for wings undergoing sinusoidal sinking oscillations. A summary table is presented as a guide to the scope and results of this paper,. This table contains the figure and equation numbers for the types of flow and plan forms considered.","url":"cran.html#doc779","title":"Calculation and compilation of the unsteady lift functions for a rigid wing subjected to sinusoidal gusts and to sinusoidal sinking oscillations."},
{"url":"cran.html#doc824","title":"On the concept of stability of inelastic systems.","description":"Drucker, D.C. And Onat, E.T. J.ae.scs., 21, 1954, 543. Simple models are employed to bring out the large and important differences between buckling in the plastic range and classical elastic instability. Static and kinetic criteria are compared and their interrelation discussed. Nonlinear behavior in particular is often found to be the key to the physically valid solution. The nonconservative nature of plastic deformation in itself or in combination with the nonlinearity requires concepts not found in classical approaches. Conversely, the classical linearized condition of neutral equilibrium is really not relevant in inelastic buckling. Plastic buckling loads are not uniquely defined but cover a range of values and are often more properly thought of as maximum loads for some reasonable initial imperfection in geometry or dynamic disturbance. The models indicate that basically the same information is obtained from essentially static systems by assuming initial imperfection in geometric forms as by assuming dynamic disturbances. One approach complements the other and both are helpful in obtaining an understanding of the physical phenomena."},
{"description":"Clarke, J.F. Coa r117, 1961. Suitable forms of the equations for the flow of an inviscid, non-heat-conducting gas in which chemical reactions are occurring are derived. The effects of mass diffusion and non-equilibrium amongst the internal modes of the molecules are neglected. Special attention is given to the speeds of sound in such a gas mixture and a general expression for the ratio of frozen to equilibrium sound speeds is deduced. An example is given for the ideal dissociating gas. The significance of the velocity defined by the ratio of the convective derivatives of pressure and density is explained. It is the velocity which exists at the throat of a convergent-divergent duct under maximum mass flow conditions, and it is shown that this velocity depends on the nozzle geometry as well as on the 'reservoir' conditions. As an illustration the phenomena of sound absorption and dispersion are discussed for the ideal dissociating gas. The results can be concisely expressed in terms of the frozen and equilibrium sound speeds, the frequency of the (harmonic) sound vibration and a characteristic time for the rate of progress of the reaction.","url":"cran.html#doc166","title":"Flow of chemically reacting gas mixtures."},
{"url":"cran.html#doc858","title":"Experimental investigation at mach numbers 3. 0 of the effects of thermal stress and buckling on the flutter of four-bay aluminium alloy panels with length-width ratios of 10.","description":"Dixon, S.C., griffith, G.E. And Bohon, H.K. Nasa tn.d921, 1961. 0 of the effects of thermal stress and buckling on the flutter of four-bay aluminium alloy panels with length-width ratios of 10. Skin-stiffener aluminum alloy panels consisting of four bays, each bay having a length-width ratio of 10, were tested at a mach number of 3.0 at dynamic pressures ranging from 1, 500 psf to 5, 000 psf and at stagnation temperatures from 300 f to 655 F. The panels were restrained by the supporting structure in such a manner that partial thermal expansion of the skins could occur in both the longitudinal and lateral directions. A boundary faired through the experimental flutter points consisted of a flat-panel portion, a buckled-panel portion, and a transition point at the intersection of the two boundaries. In the region where a panel must be flat when flutter occurs, an increase in panel skin temperature (or midplane compressive stress) makes the panel more susceptible to flutter. In the region where a panel must be buckled when flutter occurs, the flutter trend is reversed. This reversal in trend is attributed to the panel postbuckling behavior."},
{"description":"Bertram, M.H. Nasa tr.r22, 1959. 8 and 9. 6. Measurements are presented for pressure gradients induced by a laminar boundary layer on a flat plate in air at a mach number of 9.6 and for the drag of thin wings at a mach number of about 6.8 and zero angle of attack. The pressure measurements at a mach number of 9.6 were made in the presence of substantial heat transfer from the boundary layer to the plate surface. The measured pressure distribution on the surface of the plate was predicted with good accuracy by a modification to insulated-plate displacement theory which allows for the effect of the heat transfer and temperature gradient along the surface on the boundary-layer displacement thickness. The total drag of thin wings with square and delta plan forms was measured at a nominal mach number of 6.8 over a reasonably wide range of reynolds numbers. The total drag was found to be greater than can be explained by adding a classical value of laminar skin friction to the estimated pressure drag. The difference is, in general, explained by the increase in skin friction (20 to 40 percent) caused by the boundary-layer-induced pressures.","url":"cran.html#doc1355","title":"Boundary layer displacement effects in air at mach numbers of 6. 8 and 9. 6."},
{"url":"cran.html#doc921","title":"Slender-body theory-review and extension.","description":"Adams, M.C. And Sears, W.R. J. Aero. Sc. V. 20, february 1953. The approximate theory of flow about slender bodies and wings originated by munk and jones is reviewed. It is presented here in a form that emphasizes the relation to the source-sink methods of von karman and others. The extension to noncircular bodies is made for subsonic flow, paralleling ward's extension for supersonic flow. The calculation of pressures and forces and the extension of the theory to unsteady flows are reviewed, and some discrepancies in the published literature are explained. Finally, interpreting the jones slender-wing result as the first term of an expansion in powers of a breadth parameter /E.G., aspect ratio/, it is shown how a more accurate theory can be developed by carrying additional terms for both subsonic and supersonic speeds. This theory of not-so-slender wings is applied to some practical wing problems, including direct problems of flow past given wings and problems of wing design for minimum drag. The accuracy of the new results is assessed by comparison with linearized supersonic-airfoil theory for the special case of a flat delta wing."},
{"url":"cran.html#doc332","title":"Similitude of hypersonic real-gas flows over slender bodies with blunted noses.","description":"Cheng, H.K. J. Ae. Scs. 26, 1959, 575. On the basis of the hypersonic small-perturbation theory, the laws of similitude for hypersonic inviscid flow fields over thin or slender bodies are examined, and the restrictions to ideal gases with constant specific heats and to bodies with pointed noses are removed. Only steady plane or axisymmetric flows are considered. Inspection of the governing system of equations shows that a similitude law exists for flow fields, under local thermal equilibrium, having the same free-stream atmosphere. For flows of ideal gas with constant specific heats, the requirement of the same free-stream atmosphere--I.E., the same composition, pressure, and density--can be replaced by the requirement of the same ratio of specific heats. For flows over blunted wedges or cones, special laws of similitude can be obtained. Application of the similarity rules is examined for the case of hypersonic flows of an ideal gas with over flat plates with blunt leading edges, and for the case of equilibrium air flows over wedges. The possibility of simulating nonequilibrium flows over slender or thin bodies is also pointed out."},
{"url":"cran.html#doc152","title":"On the flow of compressible fluid past an obstacle.","description":"Lord rayleigh, O.M., F.R.S. It is well known that according to classical hydrodynamics a steady stream of frictionless incompressible fluid exercises no resultant force upon an obstacle, such as a rigid sphere, immersed in it. The development of a /resistance/ is usually attributed to viscosity, or when there is a sharp edge to the negative pressure which may accompany it (helmholtz). In either case it would seem that resistance involves something of the nature of a wake, extending behind the obstacle to an infinite distance. When the system of disturbed velocities, although it may mathematically extend to infinity, remains as it were attached to the obstacle, there can be no resistance. The absence of resistance is asserted for an incompressible fluid., but it can hardly be supposed that a small degree of compressibility, as in water, would affect the conclusion. On the other hand, high relative velocities, exceeding that of sound in the fluid, must entirely alter the conditions. It seems worth while to examine this question more closely, especially as the first effects of compressibility are amenable to mathematical treatment."},
{"description":"Jones, G.W. And Unangst, J.R. Naca rm l55k30, 1956. An experimental investigation has been conducted in the 26-inch langley transonic blowdown tunnel to determine effects of center-of-gravity location on the transonic flutter characteristics of a 45degree swept-back-wing plan form of aspect ratio 4.0 and taper ratio 0.6. Solid-construction models of the plan form with streamwise naca 65a004 airfoil sections and center-of-gravity locations at approximately 34 percent chord, 46 percent chord, and 58 percent chord, respectively, were fluttered at several mach numbers between 0.8 and 1.35. It was found that, for streamwise mach numbers from 0.8 to 1.0, the variation with mach number of the ratio of experimental flutter speed to a calculated incompressible flutter speed was not affected by center-of-gravity location. However, for mach numbers from 1.0 to 1.35, there was an increase in flutter-speed ratio with mach number which was different for each center-of-gravity position. Data from wings with successively more forward center-of-gravity locations showed successively larger values of flutter-speed ratio at mach numbers from 1.0 to","title":"Investigation to determine effects of center of gravity location on the transonic flutter characteristics of a 45degree sweptback wing.","url":"cran.html#doc1338"},
{"description":"Chernyi, G.G. Nasa tt f-35, 1960. Manufacturing and maintainance of ideally sharp leading edges and noses is practically impossible, hence a discrepancy arises between the theory established for sharp edges and actual flow around slightly blunted edges, where a detached shock is formed with a subsonic adjacent region. Semi-empirical method is worked out showing that the pressure distribution in the vicinity of the leading edge is the same for different thin profiles having the same shape of bluntness on their edges or noses. The data for a flat plate can be used for all of them. For moderate supersonic speed the pressure on the remaining body is practically unaffected by the nose bluntness, and can be computed from a sharp-edge theory. For high supersonic speed a slight blunting of the edge can considerably alter the pattern of flow over a large region. The method consists in replacing blunted edge by action of concentrated forces on the flow,. It is applied to blunted wedge where it shows doubling of the drag computed by classic theory, and to cones, where the drag of a blunted cone may become smaller than that of a sharp one.","title":"Effect of slight blunting of leading edge of an immersed body on the flow around it at hypersonic speed.","url":"cran.html#doc211"},
{"title":"Heat transfer to separated and reattached subsonic turbulen flows obtained downstream of a surface step.","url":"cran.html#doc651","description":"Seban, R.A., emery, A. And Levy, A. J. Ae. Scs. 1959, 809. Local heat-transfer coefficients and recovery factors are presented for separated and reattached turbulent flows as obtained by a downward step in an otherwise flat surface in a two- dimensional, subsonic, air flow. The region downstream of the step, the focus of this investigation, contained a region of separated flow with reattachment at about five step heights downstream, followed by a section of reattached flow. The salient feature of the results is the maximum in the local heat-transfer coefficient at the reattachment point, with values thereof diminishing in the separated region and also in the reattached region, where they tend toward values characteristic of turbulent boundary-layer flow. It is found that for most of the region the heat-transfer coefficient depends on the velocity to about the 0.8 power, though a decreased dependence may exist in the separated region. Recovery factors have the characteristically low values associated with separated flows, and do not attain values typical of turbulent boundary-layer flows within the downstream lengths available."},
{"description":"Nagamatsu, H.T., workman, J.B. And Sheer, R.E. J. Ae. Scs. 1961, 833. An experimental investigation on the expansion of high- temperature, high-pressure air to hypersonic flow mach numbers in a conical nozzle of a hypersonic shock tunnel has been carried out. The equilibrium temperature and pressure ranges after the reflected shock wave were 1400 to 6000 k and 100 to 1000 psia. Static-pressure measurements, which are sensitive to the state of the gas, were made along the axis of the nozzle for different reservoir conditions. These results are compared with the calculated equilibrium and /frozen/ data for the same geometry and initial reservoir conditions. For reservoir pressures greater than 500 psia, the expansion of the air in the nozzle is essentially in equilibrium up to reservoir temperatures of about 4, 500 K. For temperatures greater than almost frozen. At a given area ratio for the nozzle and reservoir pressure, the expansion process remains in equilibrium up to a certain reservoir temperature, and beyond this temperature the flow expansion deviates rapidly from the equilibrium process and approaches the frozen case.","title":"Hypersonic nozzle expansion of air with atom recombination present.","url":"cran.html#doc1230"},
{"description":"Kuhn, R.E. And Draper, J.W. Naca tn.3364, 1955. An investigation of the effectiveness of a wing equipped with large-chord slotted flaps in rotating the thrust vector of propellers through the angles required for vertical take-off and for flight at very low speeds has been conducted in the facilities of the langley 300 mph 7- by 10-foot tunnel. Under conditions of static thrust and with zero incidence between the thrust axis and the wing chord plane, the slotted flaps were effective in rotating the thrust vector upward about than 10 percent of the thrust. When an auxiliary vane was added above the wing, the thrust vector was rotated upward configuration, vertical take-off could be achieved with an initial attitude of 16 and at airplane weights up to 90 percent of the total propeller thrust. The addition of 10 incidence between the thrust axis and the wing increased the upward rotation of the thrust vector about 10. For the same turning angle, the diving moments associated with the slotted-flap configurations were approximately twice as large as the diving moments of the configurations with plain flaps and two auxiliary vanes.","title":"Investigation of effectiveness of large-chord slotted flaps in deflecting propeller slipstreams downward for vertical take-off and low-speed flight.","url":"cran.html#doc1095"},
{"description":"Gdalia kleinstein Polytechnic institute of brooklyn, farmingdale, N.Y. Recent experimental results have shown that the mixing of heterogeneous gases having an initial velocity ratio close to unity occurs faster than is predicted by classical eddy-viscosity theory. The theoretical analysis of two uniform streams of different gases but of nearly equal velocity, performed with the usual assumptions for eddy viscosity and prandtl number equal to a constant, shows that mixing will take place very slowly, I.E., at the rate corresponding to laminar diffusion. It has been suggested that the difference between analysis and experiment could be attributed to the presence of a boundary layer in the experiments. It is the purpose of this note to show that the use of the classical eddy-viscosity law, admitting the existence of a boundary layer, is not sufficient to explain the rapid mixing that is observed physically. Instead, it is shown that rapid mixing can be explained on the basis of a different eddy-viscosity law, as was suggested in ref. 1. These conclusions are obtained through application of the analysis presented briefly below.","url":"cran.html#doc1372","title":"On axially symmetric, turbulent, compressible mixing in the presence of initial boundary layer."},
{"description":"D. J. Mead, D. C. Ae. D. J. Mead, D.C.ae. This paper reviews some of the experience to date of using sandwich type structures in severe acoustic pressure environments. The methods used for testing sandwich structures for acoustic fatigue are described and their limitations considered. Experimental and theoretical work relating to the damping and mode-frequency relationships of certain sandwich configurations is also reviewed. Special attention is given to the estimation of the stress in the bond of a honeycomb sandwich panel subjected to sudden pressure fluctuations. A /uni-modal/ theory is presented, relating the mean-square bond-stress to the random exciting pressure and panel dynamic characteristics. This theory indicates that tensile bond stresses may be encountered of up to six times the local R.M.S. Exciting pressure. These must be combined with bending and shear stresses to obtain the principal stresses which precipitate bond fatigue failures. Finally, an outline is given of some of the lines of future research which should lead to the achieving of the maximum possible fatigue resistance from sandwich configurations.","title":"A note on the use of sandwich structures in severe acoustic environments.","url":"cran.html#doc720"},
{"url":"cran.html#doc435","title":"Application of similar solutions to calculations of laminar heat transfer on bodies with yaw and large pressure gradients in high speed flow.","description":"Beckwith, I.E. And Cohen, N.B. Nada tn.d625, 1961. An integral method for the rapid calculation of heat-transfer distributions on yawed cylinders of arbitrary cross-sectional shape and on bodies of revolution in high-speed flows is developed for laminar boundary layers. The method involves the quadrature of a function of the pressure distribution (assumed given) and satisfies the integral energy equation with the assumption of local similarity, wherein the actual boundary-layer profiles at every station are replaced by corresponding profiles from a family of similar solutions. The method is compared with other local similarity methods and with experimental heat-transfer data on a circular cylinder and on a body of revolution designed for large axial pressure gradients. Good agreement between theory and data is obtained and it is shown that the present integral method, in both its complete and simplified form, gives generally better agreement with the data than certain other local similarity methods. Numerical examples are presented showing that the effect of sweep and gas properties on heat-transfer distribution is small."},
{"description":"Direct measurements of supersonic local skin friction, using the floating-element technique, are presented for mach numbers from bulent flow and transition are emphasized, although some measurements in the laminar regime are included. The observed effect of compressibility is to reduce the magnitude of turbulent skin friction by a factor of two at a mach number of 4.5 and a reynolds number of about 10. The boundary-layer momentum-integral equation for constant pressure is verified within a few per cent by two experimental methods. Typical static pressure measurements are presented to show that transition can be detected by observing disturbances in pressure associated with changes in displacement thickness of the boundary layer. It is found that the turbulent boundary layer cannot be defined experimentally for values of less than about 2, 000, where is the momentum thickness. For larger values of there is a unique relationship between local friction coefficient and momentum-thickness reynolds number at a fixed mach number. The appendix compares the present measurements at m = 2.5 with experimental data from other sources.","title":"Measurements of turbulent friction on a smooth flat plate in supersonic.","url":"cran.html#doc346"},
{"url":"cran.html#doc1053","title":"Spherical cap snapping.","description":"Keller, H.B. And Reiss, E.L. J. Ae. Scs. 26, 1959, 643. A nonlinear boundary value problem for the determination of the rotationally symmetric deformations of a clamped spherical cap under external pressure is solved by finite differences. The numerical solutions are obtained by employing a previously developed iteration procedure. A special case of the difference equations is solved explicitly and yields a justification of the iteration method as well as insight into the properties of the more accurate numerical solutions. Buckled and unbuckled equilibrium states are obtained and the shape of the pressure-deflection curve which is usually assumed for these states is verified for a large class of caps. Close estimates are given for the upper and lower buckling loads and an intermediate buckling load--I.E., the /dead-weight/ load. The stresses and deflections in the buckled and unbuckled states are examined and compared with an asymptotic solution valid in the interior of very thin shells. Boundary layers are found to develop in the buckled states both as the loading increases and as the thickness of the shell decreases."},
{"description":"Lochtenberg, B.H. J.ae.scs.1960, 92. Transition to turbulence was studied in a separated laminar boundary layer on a flat plate 24 in. Long and thick. Steps with a height of to were provided at a distance of 4 to transition was observed through a hot-wire anemometer. The author concludes that transition was always initiated by tollmien-schlichting waves. Two types of transition were observed. In one type, bursts suddenly appeared in the wavy flow. The other type consists of amplification, distortion, and breaking up of the waves. Which type of transition occurs depends on the value of the following parameter.. Boundary-layer displacement thickness times step height times free-stream velocity squared divided by kinematic velocity squared. The burst type has been observed for values of this parameter larger than 4.2 x 10. The separated laminar boundary layer becomes unstable and develops waves when the critical reynolds number based on boundary-layer displacement thickness at the step location exceeds a value of 350. Some conclusions on the development of separation bubbles on air foils are drawn from the present studies.","url":"cran.html#doc1278","title":"Transition in a separated laminar boundary layer."},
{"url":"cran.html#doc195","title":"Correlation of theoretical and photo-thermoelastic results on thermal stresses in idealized wing structure.","description":"Tramposch, H. And Gerard, G. J.app.mech. 27, 1960. After a rather complete exploratory program described in previous papers, the photo-thermoelastic method was applied to the experimental evaluation of the thermal-stress theories. The new technique was correlated with several theories which analyzed the transient thermal stresses in idealized wing structures of high-speed aircraft. Various theories were investigated which represented the same idealized wing models and differed from each other only in the simplifying assumptions regarding the temperature distributions in skin and webs. The theories were evaluated by duplicating the boundary and initial conditions on plastic models and then by correlating the theories with the observed fringe orders in nondimensional form. A significant general conclusion was reached after correlating the available theories and experimental results. Owing to simplifying assumptions concerning the thermal behavior in the flanges, thermal stresses predicted by the available theories are all higher than the experimental observation. In some cases the discrepancy is as great as 30 per cent."},
{"title":"The rolling up of the trailing vortex sheet and its effect on the downwash behind wings.","url":"cran.html#doc288","description":"Spreiter, J.R. And Sacks, A.H. J. Ae. Scs. 18, 1951. The motion of the trailing vortices associated with a lifting wing is investigated by theoretical and visual-flow methods for the purpose of determining the proper vortex distribution to be used for downwash calculations. Both subsonic and supersonic speeds are considered in the analysis. It is found that the degree to which the vortices are rolled up depends upon the distance behind the wing and upon the lift coefficient, span loading, and aspect ratio of the wing. While the rolling up of the trailing vortices associated with high aspect-ratio wings is of little practical importance, it is shown that, with low-aspect-ratio wings, the trailing vortex sheet may become essentially rolled up into two trailing vortex cores within a chord length of the trailing edge. The downwash fields associated with the two limiting cases of the flat vortex sheet and the fully rolled-up vortices are investigated in detail for both subsonic and supersonic speeds. The intermediate case in which the rolling-up process is only partially completed at the tail position is also discussed."},
{"title":"Transtability flutter of supersonic aircraft panels.","url":"cran.html#doc914","description":"R. P. Isaacs Rand corp. For certain aero-elastic configurations it is possible to ascertain critical flutter conditions from static considerations alone. The idea is simply one of negation.. When the air speed exceeds a certain value statically stable equilibrium - and sometimes equilibrium itself take place. There are times when the dynamics of a situation are complex enough to defy a tractable analysis. The value of being able to indicate a flutter criterion from the simpler statics is clear. We will suppose flutter begins when some critical value of the air speed (or some parameter simply related the to) is exceeded. Here we will show that there is a critical value which, when exceeded, precludes static equilibrium. Underlying our work is the premise that these two critical values are the same. This assumption begs discussion. We will call the lowest value of our air speed parameter to preclude statically stable equilibrium of the system the transtability value. In some cases, excess of this value will ban all possibility of static equilibrium - stable or not., we will then call it a strong transtability value."},
{"url":"cran.html#doc1290","title":"Measured and calculated subsonic and transonic flutter characteristics of a 45 sweptback wing planform in air and in freon-12 in the langley transonic dynamics tunnel.","description":"Yates, E.C., land, N.S. And Foughner, J.T. Nasa tn.d1616, 1963. In order to investigate the reliability of flutter data measured in the langley transonic dynamics tunnel, an experimental and theoretical subsonic and transonic flutter study has been conducted in air and in freon-12 in this facility. The wing planform employed had an aspect ratio of 4.0, a taper ratio of 0.6, and 45 of quarter-chord sweepback. A sting-mounted full-span model was tested in addition to three sizes of wall-mounted semispan models. A wide range of mass ratio was covered by the tests in air and by flutter calculations made by the modified strip-analysis method of naca research memorandum l57l10. A limited amount of data was obtained in freon-12. Results of the tests in air and in freon-12 are in good agreement with the flutter calculations at all mach numbers. The test data compare favorably with previously published transonic flutter data for the same wing planform. The results indicate that flutter characteristics obtained in freon-12 may be interpreted directly as equivalent flutter data in air at the same mass ratio and mach number."},
{"description":"Sutton, G.P. J. Aero. Sc. V. 26, october 1959. A comparison is made of several different propulsion systems for interplanetary flight. Liquid and solid propellant rockets, propulsion systems which use nuclear energy sources, are heating rockets, magneto-plasma devices, ion rocket propulsion, solar heating rockets, and solar sails are briefly described and their current status reviewed. Engine performance requirements for different interplanetary missions are established. These several propulsion systems are then compared on the basis of several performance criteria, environmental characteristics, vehicle requirements, reliability, current status, growth potential, and efficiency. Predictions on various propulsion system capabilities and an analysis of multiple rocket engine reliability is included. It is concluded that electrical rockets are superior for long-time inter-planetary flight applications, and that chemical rockets are satisfactory for most of the immediate applications in /near/ space. None of the several propulsion schemes discussed can be rejected until further technical work has been accomplished.","title":"Rocket propulsion systems for interplanetary flight.","url":"cran.html#doc968"},
{"url":"cran.html#doc1166","title":"An investigation to determine conditions under which downwash from vtol aircraft will start surface erosion from various types of terrain.","description":"Kuhn, R.E. Nasa tn.d56, 1959. Results of an investigation with small-scale equipment of the conditions under which the downwash from a hovering vertical-take-off- and-landing (vtol) aircraft will start surface erosion indicate that the onset of erosion depends only on the dynamic pressure of the outward flow of air near the surface. For a rotor or propeller at a height of about 1 slipstream diameter above the surface, this surface dynamic pressure was found to be equal to the disk loading. For the vtol aircraft supported by a ducted fan, the surface dynamic pressure with the ducted fan exit at a height of about one-half the exit-area loading. The surface dynamic pressure decreases rapidly with increasing height of the vtol device. Erosion of sand and loose dirt started at surface dynamic pressures of 1 to 3 lb sq ft, which is in general agreement with helicopter experience. Thoroughly soaking the sand and loose-dirt surfaces increased the resistance to erosion to surface dynamic pressures of 30 to 50 lb sq ft. Spray from water started at surface dynamic pressures of 1.5 to pressures up to about 1, 000 lb sq ft."},
{"url":"cran.html#doc1025","title":"Note on creep buckling of columns.","description":"The creep of a slightly crooked section column carrying a constant load is studied theoretically. The material of the column is characterized by a strain-time relationship, under constant uniaxial stress, of the form, where is the total strain, is the constant stress, is the time, and e, a, b, and k are material constants. This form was selected because it applies to at least two alloys--75s-t6 aluminum alloy at 600 F. And A low-alloy steel at 800 and 1, 100 F. However, the analysis is intended for any material having creep properties of the same form and for which the material constants are known. A strain-time relationship under variable uniaxial stress, necessary for the column analysis, is formulated from the constant-stress properties with the aid of shanley's engineering hypotheses of creep. The analysis leads to the conclusion that the lateral deflection approaches infinity--that is, the column collapses--in finite time. Results are given showing the maximum length of time the column can support a given load before it collapses and the growth of stresses, strains, and deflections prior to collapse."},
{"description":"Bourne, D.E. And Davies, D.R. Q. J. Mech. App. Math. 11, 1958, 52. This paper presents a method of calculating the distribution of rate of heat transfer into a laminar incompressible boundary layer from the exterior surface of a long thin circular cylinder, when the surface of the cylinder is maintained at a constant temperature and the flow is parallel to the cylinder axis,. The temperature difference between the surface and the main stream is taken to be small enough to neglect buoyancy effects. A series solution, valid for small downstream distances from the nose, has been obtained already by seban, bond, and kelly. This is now extended by deriving an asymptotic series solution, valid at large downstream distances, and bridging the gap between these two series solutions by an approximate solution, based on the method used recently by davies and bourne to calculate heat transfer from a flat plate. The calculation is used to demonstrate the effect of curvature and of prandtl number on the local rate of heat transfer at various downstream distances by comparing with the corresponding flat plate results.","url":"cran.html#doc784","title":"Heat transfer through the laminar boundary layer on a circular cylinder in axial incompressible flow."},
{"title":"The homogeneous boundary layer at an axisymmetric stagnation point with large rates of injection.","url":"cran.html#doc365","description":"Libby, P.A. J. Ae. Scs. 29, 1962. This report presents a theoretical analysis of the boundary layer at an axisymmetric stagnation point with large rates of air injection. The results of a previous investigation indicated that for localized mass transfer in the stagnation region, the rates of injection are considerably greater than those usually treated. The exact stagnation-point boundary-layer equations are integrated numerically for an approximate representation of the gas properties. The two-point boundary conditions are treated in a new manner which is useful for various boundary-layer and mixing problems. The exact solutions indicate that for large rates of injection the boundary layer is closely represented by an inner isothermal shear flow and by and exterior, relatively thin region, in which the flow variables change to their free-stream values. An integral method based on profiles suggested by the exact solutions is developed and shown to lead to accurate predictions of the integral thicknesses which are of interest for a study of the downstream influence of the stagnation-point mass transfer."},
{"url":"cran.html#doc1207","title":"Supersonic airfoil performance with small heat addition.","description":"Mager, A. J.ae.scs. 1959, 99. An analytical method is presented which permits a very rapid evaluation of the acrodynamic effects arising from the addition of small amounts of heat near supersonic two-dimensional airfoils. This method applies to shockless inviscid flow without heat conduction. Also, the mechanism by which the sesired heat addition is achieved is not considered. It is shown that even small amounts of heat generate a substantial pressure rise and thus cause appreciable changes in the acrodynamic coefficients. The results of this analysis compare favorably with those obtained by a more accurate, but also more tedious, graphical method of characteristics. Two possible modes of application to an airplane design are considered from the energy requirements standpoint. In this connection, it is shown that the decrease of the required wing area resulting from heat addition may, in some cases, lead to savings in the rate of the fuel consumption. In general, however, one should not expect any substantial reduction in energy requirements resulting from the application of the wing heat addition."},
{"description":"Fox, H. And Libby, P.A. J. Ae. Scs. 1962, 921. This report presents a theoretical analysis of the boundary layer at an axisymmetric stagnation point with large rates of helium injection. The exact stagnation-point boundary-layer equations are integrated numerically with approximate representations of the gas properties. The treatment of the two-point boundary-value problem employed herein is shown to be useful for various boundary-layer and mixing problems. The exact solutions indicate that for large rates of injection the boundary layer can be represented by a thick, inner layer of constant shear, temperature, and composition and by a relatively thin outer region in which the flow variables adjust to their free-stream values. An inviscid-flow model is shown to lead to accurate predictions of this shear layer and will thus provide sufficiently accurate profiles for use in the study of the downstream influence of stagnation-point mass transfer. The heat transfer to the stagnation point is also considered. Tabulations of the eigenvalues for a variety of wall conditions and injection rates are given.","url":"cran.html#doc366","title":"Helium injection into the boundary layer at an axisymmetric stagnation point."},
{"description":"Stanitz, J.D. And Prian, V.D. Naca tn 2421, 1951. A rapid approximate method of analysis was developed for both compressible and incompressible, nonviscous flow through radial- or mixed-flow centrifugal compressors with arbitrary hub and shroud contours and with arbitrary blade shape. The method of analysis is used to determine approximately the velocities everywhere along the blade surfaces, but no information concerning the variation in velocity across the passage between blades is given. In eight numerical examples for two-dimensional flow, covering a fairly wide range of flow rate, impeller-tip speed, number of blades, and blade curvature, the velocity distribution along the blade surfaces was obtained by the approximate method of analysis and compared with the velocities obtained by relaxation methods. In all cases the agreement between the approximate solutions and the relaxation solutions was satisfactory except at the impeller tip where the velocities obtained by the approximate method did not, in general, become equal on both surfaces of the blade as required by the joukowski condition.","title":"A rapid approximate method for determining velocity distribution on impeller blades of centrifugal compressors.","url":"cran.html#doc990"},
{"description":"Scala, S.M. J. Ae. Scs. 1960, 1. A priori knowledge of the response of materials subjected to a severe aerothermal environment is essential in the space age. The successful design of space and re-entry vehicles demands that the fundamental problem of the interaction between a material and dissociated air be properly formulated and solved. In this paper, the problem of sublimation in a hypersonic environment is considered. In this study of hypersonic ablation, the pertinent conservation equations are derived and the simultaneous processes of diffusion, convection, and thermal exchange are analyzed for the vaporization of a refractory material which is subjected to the environmental conditions encountered during hypersonic reentry. For simplicity, only the forward stagnation point of an axially symmetric body is treated. It is shown that the quantity, called the effective heat of vaporization, which includes all heat absorbing or heat blocking effects, is an increasing function of flight speed, independent of body size, except where nonequilibrium vaporization effects or radiative effects appear.","url":"cran.html#doc1279","title":"Sublimation in a hypersonic environment."},
{"description":"Burgraf, O.R. J. Ae. Scs. 19, 1962. The compressibility transformation first introduced by dorod-nitzyn has been applied in this paper to the equations of the turbulent boundary layer on a flat plate, considering heat transfer and arbitrary prandtl numbers. Assuming the shear distribution to be invariant under the transformation, the stream function and the momentum equation take the proper form for incompressible flow, allowing the use of incompressible velocity profiles in the transformed coordinates. Application of crocco's method to the transformed energy equation permits integration of the energy equation resulting in a formulism remarkably similar to that proposed by eckert. Finally, the reference condition was chosen to correspond to the edge of the sublayer from considerations of the assumptions made regarding the shear-stress distribution. With this choice, the reference enthalpy is in good agreement with eckert's formula over the ordinary range of test conditions. In view of these results, the analysis may be considered to provide a theoretical basis for the reference-enthalpy method.","title":"The conpressibility transformation and the turbulent boundary layer equations.","url":"cran.html#doc538"},
{"url":"cran.html#doc32","title":"The dynamic motion of a missile descending through the atmosphere.","description":"Friedrich, H.R. And Dore, F.J. J. Ae. Scs. 22, 1955, 628. A method is presented for computing rapidly, yet accurately, the dynamic motion of a ballistic-type missile descending through the atmosphere. The equations of motion are separated into a set of /static/ trajectory equations (zero angle of attack) and a set of /rotational/ equations describing the oscillatory motion of the missile about its center of gravity. A transformation allows the rotational equations to be written in a manner analogous to the equation for an undamped oscillating spring mass system with the mass equal to unity and a time variable spring constant. For given initial conditions this equation can be solved to obtain the envelope of maximum angle of attack. An additional transformation allows the calculation of the complete oscillatory motion at any time during the trajectory as a function of the maximum angle of attack at that time. This solution shows that the maximum angle of attack of a missile descending through the atmosphere at relatively constant speed is reduced even when the aerodynamic damping is neglected."},
{"description":"Pearcey, H. H. N.P.L. Aero. 358, fm 2763. Dec. 1958. The method is based on the observation of the divergence that occurs in the variation of mean static pressure at the trailing edge of an aircraft wing at the critical stage in the development of boundary-layer separation when its influence first spreads to the trailing edge and thereby to the overall flow. The significance of the trailing-edge pressure variations and their connection with the effects that separation has on the mean and unsteady loads is discussed for various types of separation. Good prediction can be obtained from wind-tunnel tests, or warning provided in flight, for low-speed separations and for shock-induced ones up to the stage at which the shock wave reaches the trailing edge. Related divergences in wake width, lift coefficient, or shock position can also be used. Pressure measurements at other isolated points often indicate the type of separation. Certain special considerations apply for swept wings. The various flow changes that are considered are illustrated by schlieren photographs and described in an appendix.","title":"A method for predicting the onset of buffeting and other separation effects from wind tunnel tests on rigid models.","url":"cran.html#doc311"},
{"url":"cran.html#doc899","title":"Aerodynamic effects on boundary layer unsteadiness.","description":"Moore, F.K. 6th A.A.aero.conf. 1957. With a view to the study of aerodynamic problems, a review is made of boundary layer theory for a flat plate moving with a time-dependent velocity. Unsteady effects are shown to enter according to the magnitude of the ratio of time for diffusion to act throughout the boundary layer to the characteristic time of the imposed unsteadiness. It is concluded that a boundary layer may be considered quasi-steady even during extreme flight manocuvres. Generation of acoustic noise purely by boundary layer unsteadiness is generally small. Thermal and heat-transfer effects are cited. Unsteady boundary layer considerations are important in damping or amplifying certain instabilities, such as flutter of panels and stalling flutter of aerofoils. In connection with the aerofoil problem, laminar separation concepts and the stagnation-point boundary layer are described for unsteady flow. An analysis of aerofoil lift hysteresis is described, using unsteady laminar boundary layer considerations, which leads to a prediction of counter-clockwise hysteresis at maximum lift."},
{"title":"Optimum nose shapes for missiles in the super-aerodynamic region.","url":"cran.html#doc357","description":"Carter, W.J. J. Ae. Scs. 24, 1957, 527. The mechanics of the kinetic theory of gases is employed to describe the drag force on the nose of a missile moving in the super-aerodynamic region of the atmosphere. Three separate cases are considered--ideal specular reflection, specular-type reflection from a slightly rough surface, and surface absorption followed by random emission of the striking molecules. The calculus of variations is employed to obtain the differential equation of the nose shape which minimizes the drag force for each of the three cases. The resulting differential equations are then solved by a numerical procedure. The drag coefficients for the optimum nose shapes are likewise determined and these are compared with the drag coefficients given by other nose shapes. It is further shown that the drag coefficients arising when specular-type reflections occur are significantly dependent on the nose shape. When surface absorption followed by random emission occurs, the drag coefficient is not strongly dependent on either the missile nose shape or the fineness ratio of the nose."},
{"title":"Integration of the boundary layer equations.","url":"cran.html#doc150","description":"Meksyn, D. Proc.roy.S.A. 237 1956, 543. The equations of the boundary layer are integrated by an expression of the form where f(x) is a positive function with x=0 as the stationary point,. (x) is slowly varying,. The integral contains an unknown parameter which is found from the condition. The integral is evaluated by the method of steepest descent. The expressions obtained are usually divergent, except in few cases which include blasius's equation,. The divergent expressions are summed by euler's transformation. To check the procedure it is applied to falkner and skan's equation. The results obtained are very striking,. Few terms in the expansions are sufficient to obtain close agreement with hartree's laborious numerical computations. The method is also applied to the general boundary-layer equation for the case of flow past an elliptic cylinder, measured by schubauer. The results obtained are in close agreement with schubauer's measurements for the velocities, almost up to separation, for the position of the separation point,. And In satisfactory agreement downstream of separation."},
{"description":"Sibulkin, M.J. J. Ae. Scs. 19, 1952, 570. In order to determine the temperature distribution over a body moving through the atmosphere, a knowledge of the local heat-transfer coefficients is required. For slender sharp-nosed bodies, the heat-transfer coefficients are frequently approximated by using the comparable flat-plate values. However, for blunt-nosed bodies, flat-plate solutions are not applicable near the forward stagnation point. Since the greatest rate of heat transfer may occur at the forward stagnation point, its value should be investigated. In this note a theoretical solution is given for the heat transfer near the forward stagnation point of a body of revolution assuming laminar, incompressible, low-speed flow. The comparable solution for two-dimensional flow has been given by squire. In the case of a blunt-nosed body moving with supersonic velocity, the flow behind the central portion of the bow wave is subsonic, and it is possible that a low-speed solution, using as /free-stream/ conditions those behind the center of the bow wave, will apply near the stagnation point.","title":"Heat transfer near the forward stagnation point of a body of revolution.","url":"cran.html#doc1393"},
{"description":"Love, E.S. J. Ae. Scs. 26, 1959, 314. Author generalizes lees's (amr 10(1957), rev. 2601) modification of newtonian theory for blunt-nose bodies to apply to pointed- nose bodies as well. The result is expressed by sin where is the local inclination of the body surface and the subscript /max/ refers to the maximum local inclination and pressure coefficient. For blunt-nose bodies and the generalized theory reverts to lees's blunt-nose modification with given by normal shock relations. Author shows, by comparison of newtonian and generalized-newtonian theory with exact solutions, the superiority of generalized-newtonian theory. He also shows that both two-dimensional and axisymmetric shapes are correlated by this generalization. Results are presented in two figures that support author's generalization and indicate the independence of the correlation from variations in both the hypersonic similarity parameter k = m(d1) and the ratio of specific heats Y. Reviewer believes this generalization should be of interest to those engaged in development of hypersonic hardware as well as theory.","title":"Generalised-newtonian theory.","url":"cran.html#doc20"},
{"description":"Hidalgo, H. Ars J. 30, 1960. The steady-state equations of motion for a thin layer of an incompressible glassy material on the surface of an ablating and radiating blunt body are reduced to a first-order ordinary differential equation which is integrated numerically. This solution is coupled with the solution of the air boundary layer for both laminar and turbulent heat transfer with or without mass vaporization of the ablating material. The distribution of the effective energy of ablation around the body is thus obtained for a cone cylinder with a hemispherical cap that re-enters the atmosphere at hypersonic flight speeds, and has quartz as the ablating material. It is found that the ablation process from turbulent heating is more efficient than from the laminar case because of increased vaporization. This solution of the equations of motion at the stagnation point has been verified by are wind tunnel experiments. The present state of development of the are wind tunnel does not permit its use for experimental investigations of ablation around blunt bodies under turbulent heating.","title":"Ablation of glassy materials around blunt bodies of revolution.","url":"cran.html#doc553"},
{"description":"Griffith, G.E. And Miltonberger, G.H. Naca tn.3609, 1956. Temperatures and thermal stresses in typical skin-stiffener combinations of winglike structures subjected to aerodynamic heating have been obtained with the aid of an electronic differential analyzer. Variations were made in an aerodynamic heat-transfer parameter, in a joint conductivity parameter, and in the ratio of skin width to skin thickness. The results, which are presented in nondimensional form, indicate that decreasing the joint conductivity parameter lowers both the interior and the average temperature ratios, increases the peak thermal stress ratios in the skin, and may considerably increase the peak stiffener stress ratios,. Increasing the aerodynamic heat-transfer parameter decreases the interior and average temperature ratios, increases the peak skin stress ratios somewhat, but greatly increases the peak stiffener stress ratios,. And Increasing the ratio of skin width to skin thickness produces only moderate decreases in the peak skin stress ratios while moderately increasing the peak stiffener stress ratios.","url":"cran.html#doc66","title":"Some effects of joint conductivity on the temperature and thermal stresses in aerodynamically heated skin-stiffener combinations."},
{"description":"Tewfik, O.K. And Giedt, W.H. J. Ae. Scs. 1960, 721. Measurements of the heat transfer, recovery factor, and pressure distributions around a circular cylinder normal to a supersonic rarefied-air stream (total temperature 300 K.) are described for the mach number range of 1.3 to 5.7, the reynolds number range of 37 to 4, 100 and at cylinder wall average temperature levels of 90 K. And 210 K. Study of the results yielded.. (1) a correlation equation for the stagnation-point nusselt number as a function of the reynolds number just after the normal part of the detached bow shock wave,. And (2) fourier series expressions for the heat-transfer coefficient and pressure coefficient distributions in terms of the stagnation point values. In comparing these measurements with predictions based on recent analytical studies, exceptionally good agreement for the heat-transfer coefficient distribution was obtained with lees' theory. In the mach number range of 3.55 to 5.73 the pressure decreased less rapidly with distance from the stagnation point than predicted by the modified newtonian theory.","title":"Heat transfer, recovery factor and pressure distributions around a circular cylinder normal to a supersonic rarefied air stream.","url":"cran.html#doc1258"},
{"description":"Eggers, A.J. Naca R.959, 1950. With the assumptions that berthelot's equation of state accounts for molecular size and intermolecular force effects, and that changes in the vibrational heat capacities are given by a planck term, expressions are developed for analyzing one-dimensional flows of a diatomic gas. The special cases of flow through normal and oblique shocks in free air at sea level are investigated. It is found that up to a mach number of 10 the pressure ratio across a normal shock differs by less than 6 percent from its ideal gas value,. Whereas at mach numbers above 4 the temperature rise is considerably below and hence the density rise is well above that predicted assuming ideal gas behavior. It is further shown that only the caloric imperfection in air has an appreciable effect on the pressures developed in the shock process considered. The effects of gaseous imperfections on oblique shock flows are studied from the standpoint of their influence on the lift and pressure drag of a flat plate operating at mach numbers of 10 and 20. The influence is found to be small.","url":"cran.html#doc975","title":"One dimensional flows of an imperfect diatomic gas."},
{"url":"cran.html#doc439","title":"A factor affecting transonic leading edge flow separation.","description":"Wood, G.P. And Gooderum, P.B. Naca tn.3804, 1956. A change in flow pattern that was observed as the free-stream mach number was increased in the vicinity of 0.8 was described in naca technical note 1211 by lindsey, daley, and humphreys. The flow on the upper surface behind the leading edge of an airfoil at an angle of attack changed abruptly from detached flow with an extensive region of separation to attached supersonic flow terminated by a shock wave. In the present paper, the consequences of shock-wave--boundary-layer interaction are proposed as a factor that may be important in determining the conditions under which the change in flow pattern occurs. When the mach number is high enough, the attached-flow pattern exists because then the shock wave is far enough behind the leading edge to keep the influence of the high pressure behind the shock wave from extending through the boundary layer to the immediate vicinity of the leading edge and affecting the flow there. Some experimental evidence in support of the importance of shock-wave--boundary-layer interaction is presented."},
{"description":"Gupta, S. App. Sc. Res. 9, 1959. An analysis is made for the laminar free convection and heat transfer of a viscous electrically conducting fluid from a hot vertical plate in the case when the induced field is negligible compared to the imposed magnetic field. It is found that similar solutions for velocity and temperature exist when the imposed magnetic field (acting perpendicular to the plate) varies inversely as the fourth root of the distance from the lowest end of the plate. Explicit expressions for velocity, temperature, boundary layer thickness and nusselt number are obtained and the effect of a magnetic field on them is studied. It is found that the effect of the magnetic field is to decrease the rate of heat transfer from the wall. In the second part, the method of characteristics is employed to obtain solutions of the time-dependent hydromagnetic free convection equations (hyperbolic) of momentum and energy put into integral form. The results yield the time required for the steady flow to be established, and the effect of the magnetic field on this time is studied.","title":"Steady and transient free convection of an electrically conducting fluid from a vertical plate in the presence of a magnetic field.","url":"cran.html#doc267"},
{"url":"cran.html#doc1064","title":"Propeller slipstream effects as determined from wing pressure distribution on a large-scale six-propeller vtol model at static thrust.","description":"Winston, M.M. Nasa tn.d1509, 1962. During static-thrust tests of a large-scale general research model having a tilting wing and double-slotted flaps, static-pressure measurements were made on a wing segment behind one propeller to survey the effects of the slipstream. For the conditions of highest slipstream energy, the hovering end point of aerodynamic parameters for aircraft having vertical and short take-off and landing capability the tilt-wing configuration (zero flap deflection) was a 6 spanwise variation in effective angle of attack in a span of slightly less than 1 propeller diameter. Effective changes in camber on the tilt-wing configuration as a result of slipstream rotation, the radial velocity gradient, and the resultant spanwise flow were negative and had a maximum magnitude of less than 2-percent chord. For the deflected-slipstream configuration (double-slotted flaps deflected), effects important to the hovering performance were found, including a 40-percent spanwise variation in effective thrust recovery and a 20 spanwise variation in effective thrust turning."},
{"title":"Random excitation of a tailplane section by jet noise.","url":"cran.html#doc722","description":"Clarkson, B.L. And Ford, R.D. Univ. Southampton R. A.A.S.U.171. The response of a section of tailplane structure to both discrete and random noise pressures has been studied in detail. Initially the specimen was mounted behind a jet engine and the induced strains were analysed with the object of determining both the resonant frequencies and the corresponding modes of vibration. During these tests a survey was made of the spectrum and correlation pattern of the jet noise on the surface of the model. Secondly the specimen was mounted in front of a loudspeaker in an acoustics laboratory and the structural resonances were excited by means of discrete frequency sound. The mode shapes were studied in detail with the aid of a stroboscope. It is concluded that the tailplane skin on this particular piece of structure only responds to any significant degree in one structural mode. Although reasonable comparison has been obtained between the random and discrete tests, it was not possible to calculate the induced stresses using the observed mode shapes and measured pressure excitation."},
{"url":"cran.html#doc1002","title":"Preliminary investigations of spiked bodies at hypersonic speeds.","description":"Bogdonoff, S.M. And Vas, I.E. Jnl. Aero. Sci. February 1959, P. 65-74. Generally accepted solutions for the problems of hypersonic flight appear, at the moment, to be centered around the use of blunt bodies to minimize the heat-transfer rates. There are, however, several other solutions to the problem, and, as part of an exploratory study of these solutions, a detailed examination has been made of the flow over blunt bodies equipped with a spike. These tests, carried out at a mach number of about 14 in the princeton helium hypersonic tunnel, have investigated the effect of varying spike lengths for flat-faced and hemispherically-nosed axially symmetric bodies. Detailed pressure distributions have been obtained as well as heat-transfer rates. These exploratory studies have shown that the use of a spike protruding from a hemispherical-nosed cylinder at m 14 decreased the pressure level by an order of magnitude and the heat transfer to a fraction of that measured on a hemisphere without a spike. The general technique appears to hold considerable promise for hypersonic flight."},
{"description":"Newson, W.A. And Tosti, L.P. Nasa memo 11-3-58l, 1959. A wind-tunnel investigation has been made to determine the aerodynamic characteristics of a scale model of a tilt-wing vertical- take-off-and-landing aircraft. The model had two 3-blade single-rotation propellers with hinged (flapping) blades mounted on the wing, which could be tilted from an incidence of 4 for forward flight to 86 for hovering flight. The investigation included measurements of both the longitudinal and lateral stability and control characteristics in both the normal forward flight and the transition ranges. Tests in the forward-flight condition were made for several values of thrust coefficient, and tests in the transition condition were made at several values of wing incidence with the power varied to cover a range of flight conditions from forward-acceleration (or climb) conditions to deceleration (or descent) conditions the control effectiveness of the all-movable horizontal tail, the ailerons and the differential propeller pitch control was also determined. The data are presented without analysis.","url":"cran.html#doc1163","title":"Force-test investigation of the stability and control characteristics of a scale model of a tilt-wing vertical take-off and landing aircraft."},
{"description":"Lee, L.H.N. J. Ae. Scs. 29, 1962, 87. An analytical and experimental study is made for inelastic instability of initially imperfect cylindrical shells subject to axial compression. Donnell's equations and the principle of virtual work are adapted to determine the effects of initial imperfections on the buckling modes and the critical buckling stresses. The deformation theory and the incremental theory of plastic stress-strain relationships are both considered. The experimental results of ten tests on specimens made of aluminum alloy 3003-0 are presented. Comparison of experimental with theoretical results indicates that the application of the deformation theory provides a fairly accurate prediction of buckling strength, but fails in this case to yield a correct description of post-buckling behavior. On the other hand, the application of the incremental theory, which is mathematically and physically more rigorous, leads to an overestimation of buckling strength, even though initial imperfections are considered. This paradox has existed for years, and remains to be resolved.","url":"cran.html#doc760","title":"Inelastic buckling of initially imperfect cylindrical shells subject to axial compression."},
{"description":"Lambourne, N.C. And Scruton, C. Arc r + M.3054, 1956. The requirements for simulating in a wind tunnel flutter conditions appropriate to high-speed flight are discussed, and an assessment is made of the desirable features of a wind tunnel suitable for flutter testing at transonic and supersonic speeds. It is concluded that such a tunnel should have either the mach number or the stagnation pressure variable during the tunnel run, and that it is of considerable advantage, and for some purposes essential, for high stagnation pressures to be available. The stagnation pressure required to allow flight conditions to be simulated with a flutter model is considered to range from at least 2 atmospheres for transonic speeds to about 15 atmospheres for m = 4. No attempt to simulate kinetic heating is envisaged, although its effect on stiffness should be allowed for in the design of the model. To minimise uncertainties due to the variation of the model stiffness with temperature it is desirable that means for controlling the stagnation temperature should be incorporated in the tunnel.","url":"cran.html#doc876","title":"On flutter testing in high speed wind tunnels."},
{"url":"cran.html#doc679","title":"Low speed tests on 45 sweptback wings.","description":"Weber, J., brebner, G.G. And Kuchemann, D. Rae R. Aero.2374, 1958. This report contains the results of pressure measurements on three and aspect ratio 5, over an incidence range up to 10. Chordwise and spanwise lift distributions are given, mostly near the centre where, on two of the wings, modifications had been made to the section shape. It was found that altering the thickness distribution in the centre did not affect the loading but that approximately straight isobars could be obtained at values of below about 0.1. By the incorporation of twist and camber in the central part the distortion of the lift distribution in the centre could be avoided at one particular incidence, and thus the same chordwise distribution obtained over most of the span. Twist and camber alone do not improve the isobar pattern and therefore a thickness modification would be needed to give the desired lift distribution and isobar pattern at one particular incidence. The results of experimental investigations of the boundary layer and of the effect of aspect ratio will be given in a later report."},
{"description":"Almroth, B.O. And Bruch, D.O. J. Ae. Scs. 28, 1961, 573. This paper is concerned with buckling of a circular cylinder of finite length subjected to a symmetrical band of external pressure. Both experimental and theoretical results are presented. The experimental data were obtained from tests of three thin-walled steel cylinders subjected to external pressure by a pneumatic tube encircling the test cylinder at mid-length. The theory is based on the principle of minimum potential energy, and the rayleigh-ritz procedure is used to expand the displacement components in trigonometric series. Theoretical results are given in the form of graphs which show buckling pressure as a function of the following ratios.. Cylinder radius thickness cylinder length radius pressure bandwidth cylinder length theoretical results are in close agreement with existing solutions to special cases in which (1) the pressure is applied over the entire lateral surface, and (2) the pressure is concentrated along a circumferential line. The theoretical results are also in agreement with the test results.","url":"cran.html#doc891","title":"Buckling of a finite length cylindrical shell under a circumferential band of pressure."},
{"url":"cran.html#doc1194","title":"Magnetohydrodynamic flow past a thin airfoil.","description":"Cumberbatch, E., sarason, L. And Weitzner, H. Aiaa jnl. 1, 1963, 679. The steady flow of a perfectly conducting magnetohydrodynamic fluid past a thin nonconducting airfoil is studied with the usual model in which the fluid variables obey the lundquist equations linearized about a constant unperturbed flow. /hyperliptic/ flows, in which hyperbolic and elliptic fields are superimposed, are considered. Results of grad, mccune and resler, and sears and resler are extended and considered in detail for the case of an arbitrarily inclined unperturbed field. The general solution contains four line singularities along the characteristics through the ends of the body and has two arbitrary constants. By a / generalized kutta-joukowski condition, / these constants are fixed so that two of the line singularities disappear. Specifically, it is required that the solution be locally square integrable. Behavior of the exponents of the singularities is investigated by numerical computation and, in limiting cases, analytically. The singular parts of some flows are investigated numerically."},
{"title":"Viscous hypersonic similitude.","url":"cran.html#doc573","description":"Hayer, W.D. And Probstein, R.F. J. Ae. Scs. 26, 1959, 815. An extension of classical hypersonic similitude is developed which takes into account the interaction effect of the displacement thickness of the boundary layer. A basic result of this viscous similitude is that the total drag including frictional drag obeys the classical similarity law for the pressure drag. Additional similarity conditions governing viscous effects must be imposed in this similitude. Underlying the similitude is a new hypersonic boundary-layer independence principle. According to this principle, the principal part of a hypersonic boundary layer with given pressure and wall temperature distributions and free-stream total enthalpy is independent of the (high) external mach number distribution outside the boundary layer. Various features of viscous hypersonic similitudes are discussed. It is found, for example, that it applies to three- dimensional boundary-layer interaction effects on flat bodies, provided the concepts of strip theory may be applied, and provided the aspect ratio is an invariant."},
{"description":"Libby, pa. And Cresci, R.J. J. Ae. Scs. 28, 1961, 51. This report presents the results of an experimental investigation of the downstream influence of localized mass transfer in the stagnation region of a blunt body under hypersonic flow conditions. The coolant is injected through a porous plug coaxial with the centerline of symmetry of the model. The tests were carried out in a wind tunnel with a mach number of 6.0, stagnation temperatures of approximately 1, 600 R., and a stagnation pressure of approximately 600 psia. Four different gases were injected over a range of mass flows. The heat transfer on the impermeable section was measured under isothermal wall conditions,. For the higher rates of mass flow, adiabatic surface temperatures were also determined. The theoretical analysis of the boundary-layer flow is investigated in order to establish the similarity parameters for the flow system. These parameters permit the extrapolation of the test results to other flow conditions, provided that laminar flow prevails. Helium is found to be the most efficacious coolant.","title":"Experimental investigation of the downstream influence of stagnation point mass transfer.","url":"cran.html#doc84"},
{"description":"A numerical analysis is given for the solution of the general equations of thin shells of revolution subjected to rotationally symmetric pressure and temperature distributions. The basic differential equations are in a very general form, which permits the geometry of the shells considered, to be specified by discrete data points. The analysis determines elastic stresses, strains and displacements for multi-layer and multi-sectional shells of revolution. Surface loads, temperatures, thicknesses and material properties may vary arbitrarily in the meridional direction. Temperatures and material properties can also vary through the thickness. The solution is obtained by direct computation using a numerical method that employs two by two coefficient matrices,. And Hence avoids the problems of slow convergence. The solution has been programmed in a semi-algebraic language which can be used on most high speed computers. Comparisons of numerical solutions to known exact and approximate solutions of the thin shell equations are made to demonstrate the accuracy of this method.","title":"On transverse vibrations of thin, shallow elastic shells.","url":"cran.html#doc1043"},
{"title":"The calculation of lateral stability derivatives of slender wings at incidence including fin effectiveness, and correlation with experiment.","url":"cran.html#doc600","description":"Ross, A.J. Rae R.aero.2647, 1961. Comparisons are made between low-speed experimental results and estimates based on attached-flow theory for the lateral stability derivatives of slender wings at incidence, and it is found that the flow separation has little effect on the sideslip derivatives. The reduction in due to part-span anhedral is evaluated, and a semi-empirical formula is derived to account for important second-order terms. For the rotary derivatives, an attempt is made to estimate the effect of the leading edge vortices, but no satisfactory conclusions have been reached. The fin contributions to the derivatives are evaluated on the basis of treating the wing surface as a total reflection plate. Good agreement with experiment is reached for the sideslip derivatives, and for the damping-in-yaw at moderate incidences. Sidewash is found to have a large effect on the rolling derivatives, and further information on the strength and position of the leading edge vortices in non-symmetric flow is required before a complete calculation of the sidewash can be given."},
{"description":"Dyer, I. J.acous.S.am. 31, 1959, 922. Following the methods of lyon, an analysis of the vibratory response of a plate to a random pressure field is given. The pressure correlation of the random field is assumed to have a scale small compared to the plate size, to decay exponentially, and to convect with constant speed over the plate. Two cases are considered, one in which the convection speed is much less than the speed of free flexural waves in the plate, the other in which the convection speed is the same order as the flexural wave speed. The mean square plate displacement is shown to be relatively independent of convection for speeds much less than the flexural wave speed, and to increase significantly for speeds in the order of the flexural wave speed. It is shown that damping is usually, but not always, an effective means of vibration reduction. In the case of convection speeds much smaller than the flexural speed, the use of hysteretic damping for reduction of the displacement response is shown to be limited by the decay of the assumed random pressure field.","url":"cran.html#doc114","title":"Response of plates to a decaying and convecting randon pressure field."},
{"title":"Air flow in a separating laminar boundary layer.","url":"cran.html#doc1385","description":"Schubauer, G.B. Naca R.527, 1935. The speed distribution in a laminar boundary layer on the surface of an elliptic cylinder, of major and minor axes 11.78 and 3.98 inches, respectively, has been determined by means of a hot-wire anemometer. The direction of the impinging air stream was parallel to the major axis. Special attention was given to the speed distribution in the region of separation and to the exact location of the point of separation. An approximate method, developed by K. Pohlhausen for computing the speed distribution, the thickness of the layer, and the point of separation, is described in detail,. And Speed-distribution curves calculated by this method are presented for comparison with experiment. Good agreement is obtained along the forward part of the cylinder, but pohlhausen's method fails shortly before the separation point is reached and consequently cannot be used to locate this point. The work was carried out at the national bureau of standards with the cooperation and financial assistance of the national advisory committee for aeronautics."},
{"url":"cran.html#doc204","title":"A study of the application of airfoil section data to the estimation of the high subsonic speed characteristics of swept wings.","description":"Hunton, L.W. Naca rm a55c23, 1955. Estimates of the variation with mach number of the aerodynamic characteristics of swept wings are made on the basis of airfoil section data combined with span-loading theory. The analysis deals with examinations of some 26 wings and wing-body combinations ranging in sweep angle from 30 to 60 and for mach numbers between 0.6 and 1.0. Results of the study indicate that the two-dimensional section data afford good qualitative information for such high-speed aerodynamic characteristics as the variation with mach number of drag, zero-lift pitching-moment coefficient, and lift coefficient for flow separation. Quantitative estimates of the force and moment divergence mach numbers could not be made with any degree of certainty from the airfoil data alone. Somewhat improved quantitative estimates for a given configuration were obtainable by basing the estimates on the measured characteristics for a wing of similar plan form but different section, and adjusting for the effects of differences in section on the basis of section data."},
{"title":"Static longitudinal aerodynamic characteristics at transonic speeds and angles of attack up to 99degree of a reentry glider having folding wingtip panels.","url":"cran.html#doc709","description":"Olstad, W.B. Nasa tm x-610, 1961. Data are presented which were obtained from a transonic wind-tunnel investigation of a reentry glider having folding wing-tip panels. The tests were conducted at angles of attack from -4degrees to 99degrees. The reynolds number based on the mean geometric chord of the fixed planform varied from 2.35 x 10 to 2.99 x 10. The maximum lift-drag ratio for the model with the folding wing-tip panels fully extended decreased from a maximum value of 7.8 at a mach number of 0.60 to about 3.4 at mach numbers from 1.03 to 1.20. The model with the folding wing panels fully extended was stable for values of the lift coefficient from 0 up to at least 0.8. Above this lift coefficient pitch-up tendencies were observed, followed by an unstable or neutrally stable region which extended up to values of angle of attack of 50degrees or 60degrees. Deflecting the folding wing panels between ducing a significant change in the trim angle of attack or in any of the force or moment coefficients in the angle-of-attack range from 49degree to 99degree."},
{"description":"Korst, H.H. And Page, R.H. Univ. Of illinois dept. Mech. Eng. Me-tn-392-1, 1954. An analysis is made of turbulent constant pressure mixing for a compressible jet boundary, taking into consideration effects of the initial boundary layer. Velocity profiles in the mixing region are represented in a transformed plans by one-parameter families of curves, with no specification for the mixing mechanism beyond that of an exchange coefficient concept being made. The exchange coefficient is represented by the bornel function of an integral transform for the x coordinate of an intrinsic system of coordinates. This intrinsic system and the physical coordinate system are related by means of a momentum integral. Satisfactory correlation of theory and experimental low-speed data is obtained with a simple form of kernal function. An asymptotic solution, corresponding to a fully developed velocity profile in the jet boundary, allows the calculation of the mechanical energy level along the separating streamline in the jet boundary without the use of empirical information.","url":"cran.html#doc961","title":"Compressible two dimensional jet mixing at constant pressure."},
{"url":"cran.html#doc79","title":"Effects of extreme surface cooling on boundary layer transition.","description":"Jack, J.R. Naca tn.4094, 1957. An investigation was made to determine the combined effects of surface cooling, pressure gradients, nose blunting, and surface finish on boundary-layer transition. Data were obtained for various body shapes at a mach number of 3.12 and reynolds numbers per foot as high as 15x10. Previous transition studies, with moderate cooling, have shown agreement with the predictions of stability theory. For surface roughnesses ranging from 4 to 1250 microinches the location of transition was unaffected with moderate cooling. With extreme cooling, an adverse effect was observed for each of the parameters investigated. In general, the transition reynolds number decreased with decreasing surface temperature. In particular, the beneficial effects of a favorable pressure gradient obtained with moderate cooling disappear with extreme cooling, and a transition reynolds number lower than that observed on a cone is obtained. Further, an increase in the nose bluntness decreased the transition reynolds number under conditions of extreme cooling."},
{"description":"Lord, W.T. Arc r + m 3227, 1961. This paper is concerned with the design of annular supersonic nozzles to produce uniform flow in supersonic wind tunnels which are axi-symmetrical and which have an internal coaxial circular cylinder throughout. Symmetrical two-dimensional and conventional axi-symmetrical nozzles are special cases of annular nozzles. Proposals are made for design criteria sufficient to ensure that the flow inside a nozzle is free from limit lines and shock waves,. The criteria for (symmetrical) two-dimensional and (conventional) axi-symmetrical nozzles are new. The two outstanding procedures for designing two-dimensional and axi-symmetrical nozzles are generalised to apply to annular nozzles. One of the design procedures is mainly analytical and the other is mainly numerical,. The analytical expressions in both procedures are made much more complicated by the presence of the internal cylinder but the numerical process criteria and the mainly numerical design procedure are successfully applied to the design of a particular annular nozzle.","title":"A theoretical study of annular supersonic nozzles.","url":"cran.html#doc221"},
{"description":"Rudin, M. Phys.fluids, 1, 1958. When gases flow at high velocity, the rates of internal processes may not be fast enough to maintain thermodynamic equilibrium. By defining quasi-equilibrium in flow as the condition in which the temperature, pressure, density, and velocity deviate by less than a fixed, small percentage from what they would be if the flowing gas could actually be in thermodynamic equilibrium, criteria are derived for determining whether quasi-equilibrium is a stable condition in the flow. By use of excitation of molecular vibration as an example, the general properties of criteria curves are discussed and interpreted. A discussion is given of how to use these results to determine definitely whether a flow is or is not in thermodynamic equilibrium. Applications to dissociating gases, to mixtures, and to the phenomenon of /choking/ in a laval nozzle are given special consideration. For cases when application of the criteria predict nonequilibrium, equations are provided in a form useful for numerical forward integration along streamlines.","url":"cran.html#doc236","title":"Criteria for thermodynamic equilibrium in gas flow."},
{"description":"B. E. Gatewood and R. W. Gehring The ohio state university and north american aviation, inc. A strain-analysis method is derived and demonstrated for the calculation of design allowable load-strain curves for the cross section of a structure supporting axial loads and bending moments. The temperature effects of thermal stresses and changed material properties and all inelastic effects are included in the calculations so that the final curve is a design curve for the applied stresses as calculated by room-temperature elastic procedures. The method allows for sequence application and removal of load and temperature, as well as cycling of load and/or temperature. Applications are shown for a rectangular bar under temperature cycling with axial loads and/or bending moments and for a box beam with one bending-moment temperature cycle. Interaction curves beyween axial load and bending moment with inelastic effects included are given, the calculations being done on a digital computer. A procedure is given for using the method to construct design curves.","url":"cran.html#doc762","title":"Allowable axial loads and bending moments for inelastic structures under nonuniform temperature distribution."},
{"title":"Tumbling bodies entering the atmosphere.","url":"cran.html#doc719","description":"Remmler, K.L. Ars jnl. V. 32, january 1962. Pp 92-95. The equations of motion of a tumbling flat plate entering an exponential atmosphere were linearized and solved analytically to obtain a simple expression for the altitude at which tumbling would cease and libration would commence. The plate had only three degrees of freedom, and aerodynamic forces were derived from newtonian impact theory. In the linear analysis, mean values of the drag and pitch damping coefficients so that flutter occurs in the range of a low-speed wind tunnel. A particular type of construction for supersonic flutter models is described in detail. Methods of vibration testing, static testing, and flutter testing are discussed. Particular emphasis is placed on the technique of varying flow parameters rather than model parameters to precipitate flutter. The tool for varying flow parameters is the variable mach number supersonic test section of the massachusetts institute of technology blowdown wind tunnel. The aerodynamic features of the supersonic test section are presented."},
{"description":"Penland, J.A. Naca tn.3861, 1957. 86 and angles of attack up to 90. Pressure-distribution and force tests of a circular cylinder have been made in the langley 11-inch hypersonic tunnel at a mach number of based on diameter, and angles of attack up to 90. The results are compared with the hypersonic approximation of grimminger, williams, and young and with a simple modification of the newtonian flow theory. The comparison of experimental results shows that either theory gives adequate general aerodynamic characteristics but that the modified newtonian theory gives a more accurate prediction of the pressure distribution. The calculated crossflow drag coefficients plotted as a function of crossflow mach number were found to be in reasonable agreement with similar results obtained from other investigations at lower supersonic mach numbers. Comparison of the results of this investigation with data obtained at a lower mach number indicates that the drag coefficient of a cylinder normal to the flow is relatively constant for mach numbers above about 4.","title":"Aerodynamic characteristics of a circular cylinder at mach number of 6. 86 and angles of attack up to 90.","url":"cran.html#doc567"},
{"title":"Hypersonic flow over an elliptic cone: theory and experiment.","url":"cran.html#doc1231","description":"Chapkis, R.L. J. Ae. Scs. 1961, 844. By applying hypersonic approximations to ferri's linearized characteristics method, simple results were obtained for the shock shape and surface pressure distribution for an unyawed conical body of arbitrary cross section. Calculations were carried out for an elliptic cone having a ratio of major to minor axes of, and a semivertex angle of about 12 in the meridian plane containing the major axis. An experimental investigation of the flow over this body conducted at a mach number of 5.8 in the galcit hypersonic wind tunnel showed that the surface pressure distribution at zero angle of attack agreed quite closely with the theoretical prediction. On the other hand, the simple newtonian approximation predicts pressures that are too low. Surface pressure distributions and schlieren photographs of the shock shape were obtained at angles of attack up to 14 at zero yaw, and at angles of yaw up to 10 at zero pitch. At the higher angles of attack the newtonian approximation for the surface pressures is quite accurate."},
{"description":"Traugott, S.C. J. Ae. Scs. 29, 1962, 389. For a family of cones of various semiapex angles blunted by spherical caps, shock shapes and surface pressure distributions have been obtained from both the belotserkovskii method and experiment. These results are used to study convergence to conical flow. Conditions leading to both overexpansion and underexpansion on the surface with respect to the asymptotic conical pressures are described as well as conditions leading to bow shock inflection points. Conditions also exist for which a second shock may occur, or for which the sonic line cannot touch the body surface. The implications of these conditions for various blunt-body methods are discussed. For cones blunted in such a manner as to keep the flow entirely supersonic, the flow field is found to exhibit certain similarities with that for genuine blunting. This is related to the fact that the surface entropy layer for blunt bodies can be most influential, in determining surface pressure, in the interior of the flow field rather than near the surface.","url":"cran.html#doc626","title":"Some features of supersonic and hypersonic flow about blunted cones."},
{"description":"Suer, H.S., harris, L.A., skene, W.T. And Benjamin, R.J. J. Ae. Scs. 25, 1958. In a recent paper, the authors presented a statistical, semiempirical design procedure for the determination of the buckling strength of unpressurized and pressurized cylinders under axial compression. This procedure has been extended in the present paper to the bending of unpressurized and pressurized cylindrical shells and allows the calculation of the critical bending stress with a knowledge of the cylinder geometry and the internal pressure only. Because no published data could be found, an extensive series of bending tests of pressurized cylinders has been performed. These new data for pressurized cylinders are treated semiempirically together with all of the other known test data for unpressurized cylinders. Best-fit curves are presented using applicable theoretical parameters. Design curves for determining the critical buckling stress for unpressurized and pressurized cylinders in bending are then developed as 90 per cent probability curves from the test data.","title":"The bending stability of thin-- walled unstiffened circular cylinders including the effects of internal pressure.","url":"cran.html#doc839"},
{"url":"cran.html#doc948","title":"Panel flutter tests on full scale x-15 lower vertical stabilizer at mach number of 3. 0.","description":"Bohon, H.L. Nasa tn.d1385, 1962. 0. Panel flutter tests were conducted on two full-scale vertical stabilizers of the x-15 airplane at a mach number of 3.0 in the langley at dynamic pressures from 1, 500 psf to 5, 000 psf and stagnation temperatures from 300 f to 660 F. Flutter boundaries were obtained for four of the five distinct types of panels which make up the vertical sides of the stabilizers. The boundaries consisted of a flat-panel boundary and a thermally buckled-panel boundary. The flat-panel boundaries were characterized by a reduction in dynamic pressure with increasing skin temperature,. Whereas, after thermal buckling the trend was reversed. The minimum dynamic pressure for flutter occurred at the intersection of the flat-panel and buckled-panel boundaries and represented a large reduction in the dynamic pressure over the extrapolated, unstressed value. As a result of panel flutter, three of the five distinct types of panels were modified to provide the required flutter margin on the design flight dynamic pressure of the aircraft."},
{"url":"cran.html#doc40","title":"Experiments on boundary layer transition at supersonic speeds.","description":"Van driest, E.R. And Boison, J.C. J. Ae. Scs. 24, 1957, 885. Tests were conducted in the 12-in. Continuous supersonic wind tunnel of the jet propulsion laboratory, california institute of technology, to determine the effects of surface cooling on boundary-layer transition at supersonic speeds. The effects of cooling were investigated at test section mach numbers of 1.97, smooth cone in the presence of three levels of supply-stream turbulence (0.4, 2, and 9 per cent) and several single-element roughnesses at fixed axial location. Transition data were obtained optically by means of a magnified-schlieren system. The results, for the range of mach number investigated, indicate that (1) transition on a smooth cone can definitely be delayed by surface cooling, (2) transition promoted by either supply-stream turbulence or surface roughness can also be delayed by surface cooling depending upon degree of turbulence or relative roughness respectively, and (3) the adverse effects of increased turbulence and roughness decrease with increasing mach number."},
{"description":"Biot, M.A. J. Ae. Scs. 29, 1962, 568. The lagrangian thermodynamic equations of irreversible processes are extended to convective heat transfer. This generalization provides equations for the unified analysis of transient heat flow in complex systems comprising solid structures and moving fluids in either laminar or turbulent flow. The concept of a surface-heat-transfer coefficient is eliminated from the formulation. The theory is developed along two different lines. In one approach a new concept referred to as the /trailing function/ is introduced. It represents the surface-heat-transfer properties and may be evaluated by quite simple but remarkably accurate variational procedures. The method of /associated fields/ is also generalized to convective phenomena. The second line of approach extends to convective heat transfer the thermodynamic concept of entropy production for both laminar and turbulent flow. The theory amounts to an extension of the thermodynamics of irreversible processes to systems for which onsager's relations are not valid.","title":"Lagrangian thermodynamics of heat transfer in systems including fluid motion.","url":"cran.html#doc873"},
{"description":"Mangler, K.W. Arc R.9740, 1946. In a former paper (1) it has been shown that the behaviour of the laminar boundary layer on a body of revolution can be described mathematically by the same equations which are also applied to the processes in the laminar boundary layer in the two-dimensional flow along a body contour, the form of which is determined by the shape of the body of revolution. A simple relation exists between the two-dimensional boundary layers and the axially symmetrical ones. The flow had been assumed to be incompressible. In this report it shall be shown that this relation is still valid when the compressibility is taken into consideration. The distribution of velocity as well as that of temperature in the laminar boundary layer of a body of revolution can be calculated by solving the corresponding problem for the two-dimensional flow around a suitable contour. The method is made clear by the example of the supersonic flow towards a cone tip,. This example has already been treated by another method by hantzsche and wendt (2).","url":"cran.html#doc1301","title":"Compressible boundary layers on bodies of revolution."},
{"url":"cran.html#doc1245","title":"Some aspects of nonequilibrium flows.","description":"Sedney, R. J. Ae. Scs. 1961, 189. In this paper are discussed some of the general features of nonequilibrium flow. In particular, vibrational relaxation is discussed in detail. This case is somewhat simpler than dissociation and ionization but it illustrates some of the main new features of nonequilibrium flow. Those aspects of two-dimensional and axisymmetric flow behind shock waves are examined analytically which yield significant information without requiring numerical solution of the governing equations. The thermodynamics of a vibrational relaxing gas are discussed. The conditions for simulating flows are noted. Crocco's theorem and the characteristic equations are derived. Then a simple method of obtaining the initial gradients of the flow variables behind a shock is shown. These gradients are used in discussing two particular flows. An exact solution for flow over a cusped body is obtained. Flow over a wedge near the tip and far from the tip is considered. It is found that far from the tip a boundary-layer type phenomenon occurs."},
{"description":"Charczenko, N. And Hennessy, K.W. Nasa tn d-1016, 1962. The pressure distribution and pressure drag of a blunt body with a supersonic jet issuing upstream from its center were determined at free-stream mach numbers of 1.60, 2.00, and 2.85. The thrust of the jet issuing from the model nose was varied to study its effects on flow around the model and to determine variation of pressure distribution and pressure drag of the model with the thrust. At all mach numbers investigated, the pressure drag decreased with increasing retrorocket thrust until a minimum value was reached. Further increases in retrorocket thrust resulted in increases in the pressure drag. The resultant drag /pressure drag plus retrorocket thrust but excluding base and skin-friction drag/ of the model was reduced by retrorocket operation below the drag for a jet-off condition, except at very low retrorocket thrust coefficients. The flow about the nose of the blunt body was very unstable throughout the range of mach numbers and retrorocket thrust coefficients investigated.","url":"cran.html#doc994","title":"Investigation of a retrocket exhausting from the nose of a blunt body into a supersonic free stream."},
{"description":"Campbell, I.J. And Lewis, R.G. Arc cp213, 1955. Axially symmetric bodies in oblique flow. A simple picture, known from the work of I. Lotz, of the flow over the forward part of a body of revolution in oblique flow is derived here from entirely elementary considerations. The pressure at any point of the (forward part of the) body at any angle of incidence depends on three parameters whose values vary along the body. The variation of these parameters along the body can be determined from a relatively small number of wind tunnel or water tunnel measurements. The necessary water tunnel measurements have been made for four axially symmetric head shapes. Additional measurements have been made to illustrate the theoretical conclusions. The data for each head shape are adequate for a determination of the pressure coefficient at any point on the head shapes at any angle of incidence (up to 6, say). In particular they can be used to determine the peak suction at any angle of incidence and so the conditions for the onset of cavitation on the head.","title":"Pressure distributions. Axially symmetric bodies in oblique flow.","url":"cran.html#doc196"},
{"description":"Kuo, Y.A. Naca tn.2356. This report concerns the problem of constructing solutions for transonic flows over symmetric airfoils. The aspect of the problem emphasized is, of necessity, not how to form a solution for compressible flow but how to simplify the initial phase of the problem, namely, the mapping of the incompressible flow. In the case of the symmetric joukowski airfoil without circulation, the mapping is relatively simple, but the coefficients in the power series are difficult to evaluate. As a result, the problem requires simplification. Instead of the exact incompressible flow past the airfoil, an approximate flow is used, which is derived from a combination of source and sink. This flow differs only slightly from the exact one when the thickness is small. By the same method, the flow with circulation is also considered. After the incompressible-flow functions are approximated in this fashion, the numerical calculation of the corresponding compressible flow, by the hodograph theory, does not present any essential difficulty.","title":"Two dimensional transonic flow past airfoils.","url":"cran.html#doc404"},
{"description":"O'bryan, T.C. Nasa tn.d1239, 1962. A full-scale, twin-propeller vtol aircraft with a maximum gross weight of 3, 400 pounds has been operated on the ground to study the effect of downwash on several types of ground surfaces. Static operation over loose snow indicated a zone of obliterated vision ahead of the pilot in an arc of approximately 10 on each side of the plane of symmetry. An arc 10 to 45 each side of the center line was found to be an area of fair visibility while the arc from 45 to 90 was an area of poor visibility. Static operation in the presence of loose surface material indicated that the downwash cleared the area near the aircraft of these particles without recirculation or damage to any components. Short-time operation at moderate forward speed over loose gravel, with the thrust axis at an angle of in propeller-blade erosion and numerous small dents and fabric punctures in the sides of the fuselage. The propeller-blade erosion was superficial except for the leading edges where several layers of glass fiber were eroded.","url":"cran.html#doc1167","title":"An experimental study of the effect of downwash from a twin-propeller vtol aircraft on several types of ground surfaces."},
{"url":"cran.html#doc756","title":"Further comments on the inversion of large structural matrices.","description":"Charles H. Samson, jr. Professor, departments of aeronautical and civil engineering, A. And M. College of texas In a recent note, klein referred to a paper co-authored by the writer, and to ref. 3. Regarding the subject of inversion of large-order matrices, klein stated that he would show 'that the situation is not as hopeless as the anove-mentioned authors intimate'. The purpose of this note is not to take exception to klein/s conclusions, but rather to disagree with his implication that the authors of ref. 2 were pessimistic with respect to large-matrix inversions. Two general methods of analysis were treated.. The method of consistent distortion and the method of transfer matrices. The first method leads directly to a relatively large matrix of structural coefficients of both internal forces and displacements. This matrix must be inverted to solve the problem. The second method ultimately produces a relatively small matrix requiring inversion., however, to arrive at this point one must perform a number of matrix multiplications."},
{"title":"Factors affecting lift-drag ratios at mach numbers from 5 to 20.","url":"cran.html#doc1188","description":"Goebel, T.P. Martin, J.J. And Boyd, J.A. Aiaa jnl. 1963, 640. Yawed-cone working charts and an engineering method are presented and used to calculate lift-drag ratios of flat-top conical wing-body arrangements at mach numbers from 5 to 20. Viscous interaction effects are considered, but bluntness effects are neglected. Correlations of wind-tunnel data in the range show that boundary layer displacement corrections to surface pressure and skin friction are required to calculate lift-drag ratios by this method whenever is greater than 0.2. Is the freestream mach number and is the freestream reynolds number based on body length. Double- and single-type shock patterns, transition from one pattern to the other, and the variation of inner-shock position with angle of attack are described. Lift-drag ratios are calculated at selected flight design points for flat-top, conical body arrangements with triangular and hyperbolic wing planforms. The hyperbolic wing arrangement offers a potential l d benefit at mach 5 but not at mach 10 or above."},
{"url":"cran.html#doc1255","title":"The flow about a charged body moving in the lower atmosphere.","description":"Hunziker, R.R. J. Ae. Scs. 1960. The flow about an electrically charged body traveling at high speeds through the lower ionosphere is analyzed. A simple gas model composed of electrons, ions, and neutral particles is used and the hydrodynamic description given is based on maxwell's transfer equations for a mixture. The conditions under which local statistical equilibrium can be assumed are discussed, and different approaches to determine the gasdynamic force in the subsonic, supersonic, and hypersonic cases are indicated. The reciprocal action of the electric field of the flow on the body is also analyzed and a formula for the resultant electric force is given. The total force on the body is equal to the sum of the gasdynamic force and the electric force. The negative potential acquired by a plane body is also calculated. Finally, the lack of validity of debye's linearization in this case and the solution of the exterior nonlinear problem which characterize the electric potential and the electron distribution are discussed."},
{"description":"Ferri, A. And Libby, P.A. J. Ae. Scs. 24, 1957, 464. On the forebody of many practically interesting hypersonic vehicles, there is little interaction between the inviscid flow field and the boundary layer. Therefore, inviscid flow theory can be used to determine, independent of surface phenomena, the physically interesting quantities such as shock shape, shock detachment distance, sonic line shape, and pressure distribution. Furthermore, the pressure distribution so determined can then be used for the study of heat transfer, materials behavior, and other surface phenomena. Thus, for these bodies, the prandtl boundary-layer concept can be utilized for the calculation of both the inviscid flow and the boundary-layer behavior. It is the purpose of this note to point out that this concept can also be applied experimentally in order to provide, in conjunction with a conventional hypersonic wind-tunnel air supply, a means for investigating hypersonic heat transfer and surface phenomena under conditions of flight reynolds numbers.","title":"A new technique for investigating heat transfer and surface phenomena under hypersonic flow conditions.","url":"cran.html#doc37"},
{"url":"cran.html#doc1200","title":"Hypersonic viscous flow over a sweat-cooled flat plate.","description":"Tien, C.L. And Gee, C. Aiaa jnl. 1963, 159. This paper presents a theoretical analysis of the hypersonic viscous flow over a sweat-cooled flat plate. The physical system under consideration is the hypersonic laminar boundary layer over a porous flat plate with homogeneous, normal injection of a coolant into the external stream. A heat balance at the porous surface is made between the heat transferred to the surface and the heat absorbed by the coolant. The existence of similar solutions requires a nonuniform distribution of coolant injection. The method of solution consists of the integration of three simultaneous first-order equations, the momentum and the energy integral equations in the boundary layer, and the tangent-wedge approximation in the inviscid layer. First-order asymptotic formulas are given in both the strong and the weak pressure interaction regions for the induced surface pressure, the skin-friction coefficient, and the nusselt number. Numerical results for three specific cases are presented and discussed."},
{"description":"Braslow, A.L. And Knox, E.C. Naca tn.4363, 1958. A simplified method has been devised for determination of the critical height of three-dimensional roughness particles required to promote premature transition of a laminar boundary layer on models of airplanes or airplane components in a wind tunnel with zero heat transfer. A single equation is derived which relates the roughness height to a reynolds number based on the roughness height and on local flow conditions at the height of the roughness, and charts are presented from which the critical roughness height can be easily obtained for mach numbers from 0 to 5. A discussion of the use of these charts is presented with consideration of various model configurations. The method has been applied to various types of configurations in several wind-tunnel investigations conducted by the national advisory committee for aeronautics at mach numbers up to 4, and in all cases the calculated roughness height caused premature boundary-layer transition for the range of test conditions.","url":"cran.html#doc314","title":"Simplified method for determination of the critical height of distributed roughness particles for boundary layer transition at mach numbers from 0 to 5."},
{"title":"Free-flight measurements of the static and dynamic.","url":"cran.html#doc1007","description":"This report presents equations, tables, and figures for use in the analysis of helium flow at supersonic and hypersonic speeds. The contents of the report and presentation of the data parallel that of a similar reference work (naca rep. 1135) prepared for air flow. The perfect-gas relations for continuous one-dimensional flow, normal- and oblique-shock waves, and prandtl-meyer expansions are the same as for air but are presented here for completeness. The tables present the values of useful dimensionless ratios for continuous one-dimensional flow and for normal-shock waves as functions of mach number. The helium viscosity relation as a function of temperature, mass-flow rates as a function of mach number and temperature, and the reynolds number as a function of mach number and stagnation temperature are plotted. The oblique-shock characteristics of wedges and cones in helium at mach numbers of 12, 16, 20, and 24 are presented in a series of plots. Throughout all the computations, helium is considered to be a perfect gas."},
{"description":"Jones, J.J. Nasa tn.4072, 1957. An experimental investigation has been made of the attenuation of strong shock waves in air in a shock tube. Time-history measurements were made of the static pressure at several stations in the wall of the tube. The internal diameter of the tube is 3.75 inches. Shock- wave-velocity data were taken for a distance along the tube of about 120 feet. The range of the shock-wave mach number covered was from 5 to 10 and the initial pressure ahead of the shock wave varied from 5 to 100 millimeters of mercury. Hydrogen and helium were used as driver gases. A helium-driven shock wave was found to decay only about one-half as rapidly as a hydrogen-driven shock wave. The pressure level had little effect on the attenuation rate of a shock wave of given strength for the pressure range investigated. The static-pressure measurements indicated that a severe pressure gradient existed in the latter portion of the air flow. This gradient limits the testing time useful for obtaining reliable aerodynamic data.","title":"Experimental investigation of attenuation of strong shock waves in a shock tube with hydrogen and helium as driver gases.","url":"cran.html#doc1156"},
{"title":"The turbulent boundary layer on chemically active ablating surfaces.","url":"cran.html#doc1241","description":"Denison, M.R. J. Ae. Scs. 1961. Incompressible turbulent-boundary-layer analysis is extrapolated analytically to the case of a compressible turbulent boundary layer with ablation or mass injection at the surface. The effects of chemical reactions such as dissociation and recombination as well as combustion are included. The analysis applies to blunt as well as sharp bodies which are either axisymmetric or two-dimensional. When the turbulent lewis and prandtl numbers are unity, it is found that, as in the laminar case, little detailed knowledge of the chemistry inside the boundary layer is required in most instances. The conditions at the surface and the outer edge of the boundary layer are often sufficient for prediction of heat and mass transfer. Comparison is made with experiments on the combustion of graphite under turbulent flow conditions. Prediction of ablation rates within about 30 percent accuracy is obtained when empirical constants obtained from incompressible velocity profiles with no mass injection are used."},
{"title":"Investigation of local heat transfer and pressure drag characteristics of a yawed circular cylinder at supersonic speeds.","url":"cran.html#doc566","description":"Goodwin, G., creager, M.O. And Winkler, E.L. Naca rm.a55h31, 1956. Local heat-transfer coefficients, temperature recovery factors, and pressure distributions were measured on a circular cylinder at a nominal mach number of 3.9 over a range of free-stream reynolds numbers from from 0 to 44. It was found that yawing the cylinder reduced the local heat-transfer coefficients, the average heat-transfer coefficients, and the pressure drag coefficients over the front side of the cylinder. For example, at is reduced by 34 percent and the pressure drag by 60 percent. The amount of reduction may be predicted by a theory presented herein. Local temperature recovery factors were also reduced by yaw, but the amount of reduction is small compared to the reduction in heat-transfer coefficients. A comparison of these data with other data obtained under widely different conditions of body and stream temperature, mach number, and reynolds number indicates that these factors have little effect upon the dropoff of heat transfer due to yaw."},
{"description":"Garabedian, P.R. And Liebersten, H.M. J. Ae. Scs. 25, 1958, 109. A method is described for calculating examples of hypersonic flow with a detached bow shock wave past a bluff axially symmetric body. The form of the shock wave is assumed, and the analysis is based on a cauchy problem for the stream function in the subsonic region, where the motion is governed by a partial differential equation of elliptic type. Through analytic continuation into the complex domain, the cauchy problem is reformulated in such a manner that it becomes properly set in the subsonic region. This leads to a stable scheme for computation of the flow by finite differences. Numerical examples at freestream mach number 5.8 are presented in which the flow is determined throughout the subsonic region, and, in particular, the detachment distance, the location of the sonic line, and the pressure distribution along the body are calculated. These results are in excellent agreement with experimental data obtained at the california institute of technology.","url":"cran.html#doc1390","title":"On the numerical calculation of detached bow shock waves in hypersonic flow."},
{"description":"Shield, R.T. And Drucker, D.C. J. App. Mech. 28, 1961, 292. The failure under hydrostatic test of a large storage vessel designed in accordance with current practice stimulated earlier analytical studies. This paper gives curves and a table useful for the design and analysis of the knuckle region of a thin torispherical or toriconical head of an unfired cylindrical vessel. A simple but surprisingly adequate approximate formula is presented for the limit pressure, np, at which appreciable plastic deformations occur.. Where p is the design pressure, is the yield stress of the material, and n is the factor of safety. The thickness t of the knuckle region is assumed uniform. Upper and lower bound calculations were made for ratios of knuckle radius r to cylinder diameter d of 0.06, 0.08, 0.10, 0.12, 0.14, and 0.16, and ratios of spherical cap radius l to d of 1.0, 0.9, 0.8, 0.7, and 0.6. Toriconic1a heads may be designed or analyzed closely enough by interpreting in table 1 as the complement of the half angle of the cone.","url":"cran.html#doc1136","title":"Design of thin walled torispherical and toriconical pressure - vessel heads."},
{"description":"Libby, P.A. And Schetz, J.A. Aiaa jnl. 1963, 1056. The laminar diffusion and combustion of a gas injected into a high-speed uniform stream by means of a wall slot are considered. The dorodnitzin-howarth transformation is employed to reduce the boundary layer equations to incompressible form,. The nonsimilar flow field is treated by a modified oseen approximation in conjunction with the integral method. Thermal boundary conditions corresponding to an adiabatic wall and to constant wall enthalpy are discussed. The injection of homogeneous, heterogeneous, nonreactive, and reactive gases is treated. For the latter case, the models usually employed for chemical behavior, namely, frozen and equilibrium flow, are considered. The analysis is applicable to a wide variety of laminar flows, E.G., those involving cooling, thermal protection, skin-friction reduction, and supersonic deflagration. A numerical example of practical interest in connection with the venting of gaseous hydrogen boiloff from a rocket booster is presented.","url":"cran.html#doc1180","title":"Approximate analysis of the slot injection of a gas in laminar flow."},
{"description":"Lighthill, M.J. Phil. Mag. 40, 1949, 1179. A method is described for treating some of the characteristically non-linear problems of physics, in particular those involving a non-linear partial differential equation for which an approximate linearization is permissible everywhere except in a limited region, such as the neighbourhood of (5) a singular characteristic of the approximate solution, or of approximation is valueless. The method involves a transformation of an independent variable, which is determined progressively with successive approximations to the solution.. Only one step being necessary if a first approximation valid uniformly be obtained. The method is most easily understood in its application to simple first order ordinary differential equations, which are studied in detail in 2 and 3 as a preparation for the extension to more complicated problems in 4, 5 and 6. Physically, the longest section, 6, concerns the /spread/ of a progressive wave at infinity, an important and essentially non-linear process.","title":"A technique for rendering approximate solutions to physical problems uniformly valid.","url":"cran.html#doc777"},
{"description":"Bressette, W.E. And Leiss, A. 39. An investigation at a free-stream mach number of 1.39 utilizing a blowdown-type tunnel was made to determine the effects of a propulsive jet on a zero angle-of-attack wing surface located in the vicinity of both a choked convergent nozzle and a convergent-divergent nozzle. Staticpressure surveys were made on a flat surface that was located in the vicinity of the propulsive jet. The nozzles were operated over a varied range of both exit static- and total-pressure ratios at different within the scope of this investigation, it was found that shock waves, formed in the external flow because of the presence of the jet exhaust, impinged on the flat surface and greatly altered the pressure distribution. An integration of this pressure distribution for the choked convergent nozzle, with the location of the propulsive-jet exit varied from 1.747 jet-exit diameters to 4.981 jet-exit diameters below the wing surface, resulted in a positive incremental normal force on the wing at all positions.","title":"Investigation of jet effects on a flat surface downstream of the exit of a simulated turbojet nacelle at a free-stream mach number of 1.39.","url":"cran.html#doc693"},
{"title":"Rayleigh's problem for a cylinder of arbitrary shape.","url":"cran.html#doc787","description":"Hasimoto, H. J. Physical soc. Of japan, vol. 9 /4/, 1954, P. 611-619. The motion of an incompressible viscous fluid generated by a cylinder of arbitrary cross-sectional form which is started to move suddenly from rest with uniform velocity in the direction of its length is considered formulae in powers of are derived for the velocity distribution /valid in the vicinity of the cylinder/ and for the frictional drag on the cylinder, correct to the order of a, where a is the characteristic length of the cross section, v is the kinematic viscosity, and t is the time. These formulae are given in terms of only the analytic function which maps conformally the region outside the cross section of the cylinder onto the region outside the unit circle, and of certain integrals e which are common to any arbitrary cylinder. In particular, when a is sufficiently small, the total frictional drag on the cylinder per unit length is expressed as, irrespective of the cross-sectional form, where b 2 and y 0.5772.../euler's constant/."},
{"description":"Windenburg, D.F. And Trilling, C. Asme trans. 56, 1934, 819. This paper discusses the collapse by instability of thin-walled cylindrical vessels subjected to external pressure. The most important of the theoretical and empirical formulas that apply to this subject are presented in a common notation. A new and simple instability formula is developed. Three classes of tubes are considered.. Tubes of infinite length,. Tubes of finite length with uniform radial pressure only,. And Tubes of finite length with both uniform radial and axial pressure. Collapsing pressures calculated by the various formulas are presented in tabular form as a means of comparing the formulas. The formulas are discussed briefly and checked against the results of tests conducted at the U. S. Experimental model basin for the bureau of construction and repair, navy department. This paper is a sequel to one previously published as a part of the work of the A.S.M.E. Special research committee on the strength of vessels under external pressure.","title":"Collapse by instability of thin cylindrical shells under external pressure.","url":"cran.html#doc1125"},
{"description":"Michael, W.H. Naca tn.3472, 1955. An experimental study has been made to investigate some aspects of the nature of the flow around delta wings. Vapor-screen, pressure-distribution, and ink-flow studies were made at a mach number of 1.9 on a series of semispan delta-wing models with slender wedge airfoil sections and very sharp leading edges. The models had semiapex angles ranging from 5 to 31.75. Separated regions of vorticity existed along the chords of all the wings in the series tested. Concentrated vortex cores were found only on wings of very small semiapex angles. For wings with medium and large semiapex angles, the separated vorticity was concentrated in a region extending over the outboard part of the span and lying close to the wing upper surface. The results show that theoretical aerodynamic calculations, such as those in naca tn 3430, utilizing a single, separated vortex pair above the wing upper surface to represent the separated vorticity can be applied at supersonic speeds for very slender wings.","title":"Flow studies on flat plate delta wings at supersonic speeds.","url":"cran.html#doc464"},
{"description":"Bush, W.B. J. Ae. Scs. 1960, 49. The laminar boundary-layer equations are formulated and solved for a flat plate in high-speed compressible air flow where equilibrium dissociation and ionization are assumed and where there is an applied magnetic field having its component normal to the plate proportional to. The skin-friction and heat-transfer characteristics are determined for free-stream velocities of up to 17, 500 meters sec. And Magnetic fields of up to about the results show that the skin friction and heat transfer at a given free-stream velocity decrease with increasing magnetic field strength, and the percentage reduction is constant along the length of the plate. They also exhibit the same hysteresis behavior as was first found in the case of magnetoaerodynamic couette flow,. However, for the flat plate the hysteresis effect disappears at a higher mach number. Furthermore, it was found that the reduction in heat transfer with increasing field strength is opposite in behavior from that for couette flow.","title":"Compressible flat-plate boundary-layer flow with an applied magnetic field.","url":"cran.html#doc1282"},
{"description":"Jones, E.E. Q.J.mech.app.math. 12, 1959, 191. The stream function for the shear flow with hyperbolic velocity profile past an elliptic cylinder has been determined as an infinite series of mathieu functions. It is found that the stagnation streamline of the flow is displaced towards a region of higher velocity, this displacement increasing the main stream, (2) as the stream becomes progressively non-uniform, (3) with increase of minor axis length when the major axis length remains invariant. In each case the displacement reaches a limiting value as the cylinder moves away from the axis of symmetry of the stream. These limiting values are reached at critical distances from the axis of symmetry, which decrease as the stream becomes progressively non-uniform, but these distances are approximately independent of incidence. The pressure coefficients and the resultant force and moment coefficients associated with the cylinder have also been obtained, and investigated numerically for the flat plate type of cylinder.","title":"The elliptic cylinder in a shear flow with hyperbolic velocity profile.","url":"cran.html#doc116"},
{"title":"A compressor routine test code.","url":"cran.html#doc237","description":"N. A. Dimmock Communicated by the deputy controller aircraft (research and development), ministry of aviation The routine testing of aircraft-type compressors.dash in the main, axial-flow, multi-stage compressors.dash requires a compromise between research accuracy and the practical considerations. This test code is the outcome of a survey of compressor testing techniques and instrumentation, initiated and subsequently discussed and endorsed by the aerodynamics sub-committee of the gas turbine collaboration committee. The code aims at defining methods of measurement and weighting whereby compressor performance can be obtained sufficiently accurately for a realistic and direct comparison to be made between one compressor and another. The measurement of a quantity at a point in the fluid flow, and the averaging and weighting of such measurements have been treated separately as far as is possible. The recommendations are given in the main text, whilst additional discussion on these is put into the appendices."},
{"description":"Lindholm, U.S., kana, D.D. And Abramson, H.N. J. Ae. Scs. 29, 1962, 1052. Resonant breathing frequencies and mode shapes are determined experimentally for a thin-walled, circular cylindrical shell containing a nonviscous incompressible liquid. The resonant frequencies determined for the full shell are in good agreement with those predicted by reissner's shallow-shell vibration theory with the inclusion of an apparent-mass term for the liquid. The effect of the internal liquid on the shell mode shapes is significant only for the partially full shell. In this case the circumferential node lines tend to shift toward the bottom or filled portion of the shell. Excitation of low-frequency liquid-sloshing motion by high-frequency forced oscillation of a partially filled shell occurred in many cases. This low-frequency liquid response is tentatively explained as being excited by a beat frequency in the forced oscillation. A similar type of response has been reported by yarymovych in axially excited rigid tanks.","title":"Breathing vibrations of a circular shell with an internal liquid.","url":"cran.html#doc764"},
{"title":"A simplified method of elastic stability analysis for thin cylindrical shells.","url":"cran.html#doc843","description":"Batdorf, S.B. I. Donnell's equation. Naca tn.1341, 1947. The equation for the equilibrium of cylindrical shells introduced by donnell in naca report no. 479 to find the critical stresses of cylinders in torsion is applied to find critical stresses for cylinders with simply supported edges under other loading conditions. It is shown that by this method solutions may be obtained very easily and the results in each case may be expressed in terms of two nondimensional parameters, one dependent on the critical stress and the other essentially determined by the geometry of the cylinder. The influence of boundary conditions related to edge displacements in the shell median surface is discussed. The accuracy of the solutions found is established by comparing them with previous theoretical solutions and with test results. The solutions to a number of problems concerned with buckling of cylinders with simply supported edges on the basis of a unified viewpoint are presented in a convenient form for practical use."},
{"description":"Ashwell, D.G. Proc. Roy. Soc. A, 214, 1952, 98. Part 1. From a general equation governing the bending of thin elastic plates into certain types of surfaces of revolution are derived expressions for the behaviour of rectangular plates with initial curvatures, subjected to pure bending about one axis. It is found that such plates exhibit the type of instability characteristic of thin-walled structures which depend for their stiffness on curvature. Curves are drawn showing the deformation suffered by such plates, and an expression for the critical bending moment at which instability occurs is obtained. Experimental results show satisfactory agreement. Part 2. The analysis of part 1 is extended to deal with the case of flat square or rectangular plates loaded by distributed bending moments applied to all four edges. Curves are drawn to describe their behaviour, and they are found to exhibit the characteristic instability displayed by thin-walled curved structures. Experimental verification is satisfactory.","title":"A characteristic type of instability in the large deflections of elastic plates.","url":"cran.html#doc1363"},
{"url":"cran.html#doc718","title":"Means and examples of aeronautical research in france at onera.","description":"Maurice roy The twenty-second wright brothers lecture office national d'etudes et de recherches aeronautiques Cosmonautics is currently very much to the forefront in the news. It embraces and extends aeronautics, and i would like to propose including both, at least on certain occasions, under a general denomination of /aerocosmonautics/. In your country, the sciences and technology of space are subjects which have been backed by initial advances and abundantly treated. Since france has not yet launched any artificial satellite or built any circumlunar space vehicle, i propose to confine myself here to the field of aeronautics, where there is still so much progress of manifest utility to accomplish. I shall accordingly content myself with presenting some examples of aeronautical research and experiments undertaken in my country by onera, a body whose mission is akin to that of the illustrious naca, now nasa, but bearing in mind the considerable difference between the scales of the respective resources."},
{"url":"cran.html#doc1074","title":"Theoretical and experimental investigation of second-order supersonic wing-body interference.","description":"Landahl, M., drougge, G. And Beane, B.J. J. Aero. Sc. V. 27, september 1960. Pp 694-702. Approximate second-order solutions for the supersonic flow around wing-body combinations are calculated, using two different theoretical models small and the wing sweep small in comparison with that of the mach cone are considered. The analysis is restricted to such high mach numbers that m-2 1, and an approximate formula common to the two models is then found for the second-order interference term. This formula can also be used to correct experimental pressure distributions for the effect of nonuniformities in the wind-tunnel flow. In order to test the theory, wind-tunnel experiments on non-lifting cone-cylinder bodies in combination with wings of simple shapes were performed. Pressure distributions were measured at m 3 and m 4, both around the bodies and on the wings separately, as well as in combination, and it was found that the second-order interference was predicted reasonably well by the simplified theory."},
{"description":"Portnoy, J. Aero. Quart. 11, 1960, 387. The methods of the operational calculus are used to obtain a linear approximation to the shape of the mean camber surface of a quasi-cylinder in a supersonic flow in terms of its shell thickness and loading distributions. The analysis deals with a generalised quasi-cylinder ,. That is one which, although lying close to a mean cylinder, need not possess axial symmetry. The quasi-cylinder is also permitted to be within the small disturbance field of other separate components, E.G. A centre-body. Because the linearised theory is inadmissable for internal duct flows close to and beyond the first reflected characteristic cone, the present solution is likewise invalid close to and beyond the position where this characteristic meets the mean cylinder. The work given here enables the camber shapes of /ring-wings/, which have been used theoretically to reduce or even nullify the wave-drag of a central slender-body, to be found. An example illustrates the general method.","url":"cran.html#doc428","title":"The quasi-cylinder of specified thickness and shell loading in supersonic flow."},
{"description":"Kanwal, R. J.math.mech. 9, 1960, 681. In the earlier attempts at finding the jump conditions across a hydromagnetic shock wave (1, 2, 3) various simplifying assumptions regarding the shape of the shock and the dimensions and the character of the motion are made. From that analysis it is possible to write down the jump conditions in a higher degree of generality (4). The shock conditions for magnetohydrodynamic flows can, however, be derived in their full generality with the help of the transport equation as used by thomas (5) in the derivation of shock conditions in conventional gas dynamics. The purposes of this paper are.. Cover the present more general case. That every flow and field quantity downstream from the shock wave is expressible separately in terms of the known values of these quantities upstream from the shock wave. In this rearranged form of the equations, various effects of the shock wave can be easily read off. The shock conditions along the same lines as in conventional gas dynamics.","title":"On magnetohydrodynamic shock waves.","url":"cran.html#doc190"},
{"description":"Hama, P.R., recesso, J.V. And Christiaens, J. J. Ae. Scs. 1959, 335. With a view to studying the effect of strong transverse curvature on boundary-layer problems, the axisymmetric free- convection problem along a vertical thin cylinder is investigated theoretically as well as experimentally. A theory is developed as an extension of the pohlhausen solution of a thick axisymmetric laminar boundary layer by mark and by glauert and lighthill. Experiments consist of a thermocouple survey of the temperature field over an electrically-heated brass cylinder of diameter and 10 ft. Height and an interferometric study of the density field over a bare tungsten wire of 0.02-in. Diameter and 5 ft. Height. The thermal-layer thicknesses are about five and fifty times the radii of the cylinders, respectively. Experimental results of the local heat-transfer coefficient are in excellent agreement with the theory. This, in turn, justifies the theories of laminar boundary layer along a thin cylinder, at least indirectly.","title":"The axisymmetric free-convection temperature field along a vertical thin cylinder.","url":"cran.html#doc912"},
{"description":"Owen, P.R. And Zienkiewicz, H.K. J.fluid mech. 2, 1957, 521. A nearly uniform shear flow was obtained in the working section of a wind tunnel by inserting a grid of parallel rods with varying spacing. The function of such a grid is to impose a resistance to the flow, so graded across the working section as to produce a linear variation in the total pressure at large distances downstream without introducing an appreciable gradient in static pressure near the grid. A method of calculating a suitable arrangement of the rods is described. Although this method is strictly applicable only to weakly sheared flows, an experiment made with a grid designed for a shear parameter as large as 0.45 gave results in close agreement with the theory. There was no evidence from the experiment of any large-scale secondary flow accompanying the shear--a danger inherent in an empirical attempt to grade the resistance of the grid--nor was any tendency observed for the shear to decay with increasing distance from the grid.","url":"cran.html#doc109","title":"The production of uniform shear flow in a wind tunnel."},
{"description":"Coltrane, L.C. Naca rm l58a16, 1958. 35 to 2. 15. A fineness-ratio-2.71 right circular cylinder and a fineness- ratio-been tested in free flight over a mach number range of 0.35 to 2.15 and a reynolds number range of 1 x 10 to 12 x 10. Time histories, cross plots of force coefficients, rolling velocity, and longitudinal-force coefficient are presented for both cylinders. In addition, cross plots of moment coefficients and plots of the normal-force curve slope and the aerodynamic center are presented for the fineness-ratio-2.71 cylinder. The average aerodynamic center of the right circular cylinder moved rearward with decreasing speeds until at the subsonic mach numbers it remained approximately constant and comparisons of the drag data of this test with wind tunnel and other free-flight data show good agreement. An appreciable decrease in drag was observed when the data of the present test of the rounded nose cylinder were compared with data of a right circular cylinder of a similar configuration.","title":"Investigation of two bluff shapes in axial free flight over a mach number range from 0. 35 to 2. 15.","url":"cran.html#doc812"},
{"url":"cran.html#doc1110","title":"On supersonic flow past a slightly yawing cone.","description":"Stone, ah. J. Math. Phys. 27, 1948, 67. This paper is concerned with the motion of a circular cone, of not too blunt an angle, through air at high speed. If the direction of motion of the cone coincides with its axis of symmetry, the resulting air flow is well known. Here we consider the perturbation produced by a small /yaw/--I.E., the case in which the cone is moving not quite in the direction of its axis. The results are confirmed experimentally, and have applications to ballistics, though we are not concerned with the latter here,. They may also be useful as providing a check on various approximate methods of wider applicability. The square of the yaw is neglected--an approximation of which the validity is discussed. (similar methods can be applied to the second-order effects of the yaw, which are also of ballistic significance,. But the computations have not yet been completed.) it should be observed that, because of the lack of symmetry, the flow will be neither irrotational nor isentropic."},
{"description":"Amick, J.L. Nasa tn.d753, 1961. 86 and angles of attack to 100. Measured pressure distributions on cones are compared with modified newtonian theory. Deviations as large as 14 percent of the stagnation pressure behind a normal shock are found. By combining empirical results for cylinders normal to the flow with newtonian concepts, a method of calculating pressures on cones at high angles of attack is developed. Calculations by this method differ from the experimental results on sharp cones by only 2 percent of the stagnation pressure behind a normal shock. For blunted cones, additional deviations up to 8 percent are noted near the nose. Schlieren pictures of the flow show an attached shock on the sharp of attack. Detachment of the shock appears to be associated with the attainment of sonic speed immediately behind the shock. An orifice size effect is found which can increase the indicated pressure above the true value, if the orifice width is greater than one-tenth the local radius of curvature.","title":"Pressure measurements on sharp and blunt 5 and 15 half-angle cones at mach number 3.86 and angles of attack to 100.","url":"cran.html#doc58"},
{"description":"Marguerre, K. Naca tm.1302, 1951. The report is a first attempt to devise a calculation method for representing the buckling behavior of cylindrical shells of variable curvature. The problem occurs, for instance, in dimensioning wing noses, the stability behavior of which is decisively influenced by the variability of curvature. The calculation is made possible by simplifying the stability equations (permissible for the shell of small curvature) and by assuming that the curvature as a function of the arc length s can be represented by a very few fourier terms. We evaluated the formulas for the special case of an ellipse-like half oval with an axis ratio under compression in longitudinal direction, shear, and a combination of shear and compression. However, the results can also be applied approximately to an unsymmetrical oval-shell segment under compression, shear, and bending so that the numerical values contained in the diagrams 10 to 12 represent directly dimensioning data for the wing nose.","title":"Stability of the cylindrical shell of variable curvature.","url":"cran.html#doc929"},
{"description":"Li, t-Y. J.aero.scs. 23, 1956, 1128. Theoretical investigation is considered of the two-dimensional steady flow field at large distance from a finite object set in a viscous incompressible fluid. Study is made of coordinate-type expansions for pressure and velocity for large r, uniformly in, for fixed reynolds number, assuming exact boundary conditions at infinity and regularity of flow with zero net mass flow across a simple curve enclosing the object. Mathematical nature of the distinction between parameter and coordinate-type expansions is discussed with description of inner and outer expansions and matching techniques. A feature of the expansion procedure is the introduction of an artificial parameter. Inner and outer expansions are matched with the aid of known solutions of the navier-stokes equations. Analysis requires simple consideration of the heat and laplace equations without resort to special methods. Paper is worth studying by those interested in asymptotic expansion procedures.","title":"Effects of free stream vorticity on the behaviour of a viscous boundary layer.","url":"cran.html#doc128"},
{"url":"cran.html#doc829","title":"Stability of thin-walled tubes under torsion.","description":"Donnel, L.H. Naca R.479, 1933, 12. In this paper a theoretical solution is developed for the torsion on a round thin-walled tube for which the walls become unstable. The results of this theory are given by a few simple formulas and curves which cover all cases. The differential equations of equilibrium are derived in a simpler form than previously found, it being shown that many items can be neglected. The solution obtained is length ratio is zero and infinite, and is a good approximation for intermediate cases. The theory is compared with all available experiments, including about 50 tests made by the author. The experimental-failure torque is always smaller than the theoretical-buckling torque, averaging about 75 percent of it, with a minimum of 60 percent. As the form of the deflection checks closely with that predicted by theory and the experiments cover a great range of shapes and materials, this discrepancy can reasonably be ascribed largely to initial eccentricities in actual tubes."},
{"url":"cran.html#doc474","title":"Laminar mixing of a compressible fluid.","description":"Dean R. Chapman A theoretical investigation of the velocity profiles for laminar mixing of a high-velocity stream with a region of fluid at rest has been made assuming that the prandtl number is unity. A method which involves only quadratures is presented for calculating the velocity profile in the mixing layer for an arbitrary value of the free-stream mach number. Detailed velocity profiles have been calculated for free-stream mach numbers of 0, 1, 2, 3, and 5. For each mach number, velocity profiles are presented for both a linear and a 0.76-power variation of viscosity with absolute temperature. The calculations for a linear variation are much simpler than those for a 0.76-power variation. It is shown that by selecting the constant of proportionality in the linear approximation such that it gives the correct value for the viscosity in the high-temperature part of the mixing layer, the resulting velocity profiles are in excellent agreement with those calculated by a 0.76-power variation."},
{"url":"cran.html#doc310","title":"Hypersonic viscous flow over a flat plate.","description":"Lees, L. And Probstein, R. F. Princeton univ. Aero eng. R195, 1952 (abstract by E.M.keen) In dealing with the steady laminar viscous flow over a semi-infinite flat plate some of the following topics are discussed. The streamline in the boundary layer over a leading edge of given thickness. The rate of growth of the boundary layer in the main stream, and causes of pressure variations. Asymptotic solutions for thn downstream flow region, including the joining interaction of shock waves at the leading edge. Pressure variations in the interanl viscous flow layer and in external inviscid flow considered as prandtl meyer flow. In cases of streamline deflection, the free stream mach number, zero pressure gradient, and surface pressure distribution. Asymptotic solutions for cases of fluid injection of a cool gas. Prandtl heat transfer. The joining interaction between the external inviscid flow and the internal viscous flow layer. Steady laminar hpyersonic viscous flow over a flat wedge and a cone."},
{"title":"A low density wind tunnel study of shock wave structure and relaxation phenomena in gases.","url":"cran.html#doc171","description":"Sherman, F.S. Naca tn.3298. The profiles and thicknesses of normal shock waves of moderate strength have been determined experimentally in terms of the variation of the equilibrium temperature of an insulated transverse cylinder in free-molecule flow. The shock waves were produced in a steady state in the jet of a low-density wind tunnel, at initial mach numbers of 1.72 and 1.82 in helium and 1.78, the shock thickness, determined from the maximum slope of the cylinder temperature profile, varied from mean free path in the supersonic stream. A comparison between the experimental shock profiles and various theoretical predictions leads to the tentative conclusions that.. (1) the navier-stokes equations are adequate for the description of the shock transition for initial mach numbers up to 2, and (2) the effects of rotational relaxation times in air can be accounted for by the introduction of a /second/ or /bulk/ viscosity coefficient equal to about two-thirds of the ordinary shear viscosity."},
{"description":"Romeo, D.J. And Sterrett, J.R. Nasa tn d-743, april 1961. An investigation of the effects of the interaction ahead of a two-dimensional sonic jet exhausting perpendicularly into a mach number were made at an angle of attack of 0degree at a reynolds number per foot of approximately 6 x 10 and with conditions of both transitional and turbulent separation on the flat plate. The ratio of jet stagnation pressure to free-stream static pressure was varied from 8 to 460 and the jet slot width was varied from 0.001 to 0.05 inch. The force ratio due to reaction of jet/, calculated ahead of the jet, was sizable and varied from 0.5 to 9. In general, the ratio increased with increasing pressure ratio and decreasing slot width. For the turbulent boundary-layer separation tests it was found that the first peak pressure and the chordwise pressure distribution of the separated boundary layer ahead of the jet were similar to those for a separation caused by a forward-facing step at the same test conditions.","url":"cran.html#doc972","title":"Aerodynamic interaction effects ahead of a sonic jet exhausting perpendicularly form a flat plate into a mach number 6 free stream."},
{"description":"Lord, W.T. And Brebner, G.G. Aero.quart. 10, 1959, 79. Some recent theoretical work on slender pointed wings at zero lift is co-ordinated and extended. The wings considered may have any pointed plan form shape, provided that the trailing edge is straight and unswept. The root section profile and cross-section shapes are arbitrary, provided that, on any one wing, the latter are /descriptively similar/ (diamond or parabolic biconvex for instance), though not necessarily geometrically similar. The chief aim of the work is to find wings with simple geometry, low wave drag and pressure distributions which are unlikely to be seriously affected by viscous effects. Wave drag and pressure distributions are calculated by slender-wing theory. General formulae, which are both simple and instructive, are given for the wave drag and the overall pressure distribution, with particular emphasis on the root pressure distribution. Results for a number of wings of special interest are presented and discussed.","url":"cran.html#doc147","title":"Supersonic flow past slender pointed wings with ?similar? cross sections at zero lift."},
{"description":"H. Hoshizaki and H. J. Smith Missile and space division, lockheed aircraft corporation, sunnyvale, calif. An effective means of protecting the surface of a hypersonic re-entry vehicle is to inject small quantities of a lightweight gas into the boundary layer through a porous wall. This process, which is known as mass-transfer cooling, protects the surface in two ways. First of all, as the injected gas or coolant passes from the reservoir through the wall to the surface, a considerable quantity of heat is absorbed as its temperature is raised from the reservoir temperature to the wall surface temperature. Characteristically, lightweight gases have relatively high specific heats. Secondly, the transfer of mass and enthalpy by convection and diffusion normal to the surface alters the characteristics of the boundary layer in such a manner as to reduce the temperature gradient at the wall, and, hence, the conductive heat transfer at the wall. This is sometimes referred to as the blowing effect.","url":"cran.html#doc353","title":"The effect of helium injection at an axially symmetric stagnation point."},
{"description":"Charts of thermodynamic properties for equilibrium air are presented with sufficient accuracy to permit the calculation of flow parameters in hypersonic nozzles operating at stagnation temperatures up to 4, 950 r and pressures up to 1, 000 atm. Flow parameters calculated from these charts are presented for a series of stagnation temperatures between use of these parameters, it is possible to calibrate a nozzle in the conventional way. A method is also presented from which the flow parameters for conditions other than those chosen herein may be calculated. Real-gas effects on the calculation of a hypersonic nozzle contour are shown by an example calculation in which the nozzle contour for mach number 12 was determined by including real-gas effects, and this contour was compared with one calculated by ideal-gas considerations. Also presented are the approximate limiting mach numbers at which equilibrium air will just condense for various combinations of stagnation temperatures and pressures.","title":"Free-flight measurements of the static and dynamic.","url":"cran.html#doc1009"},
{"url":"cran.html#doc804","title":"A flight test investigation of the sonic boom.","description":"Mullens, M.E. Afftc-tn-56-20, air res. And Dev. Command, U.S.A.F., 1956. The /sonic boom/ as it is now popularly called, has become the center of considerable interest during the past few years because of widespread public disturbance and possible damage that can result from it. In the hopes of minimizing this disturbance and to extend the general knowledge of the shock waves which produce the booming noise, the aeronautical research laboratory, wright air development center, has initiated an extensive research program to study the sonic boom phenomenon. This report presents the results of flight tests undertaken as one phase of this program. The tests had as their objective the determination and measurement of the shock wave pressure pattern surrounding an f-100 aircraft in level supersonic flight. The flight tests were conducted at the air force flight test center, edwards air force base, california, under the authority of air research and development command test directive no. 5524-f1."},
{"description":"V. I. Weingarten Space technology laboratories, inc., los angeles, calif. Now with aerospace corp., los angeles, calif. Two problems illustrating the effect of nonuniformity of loading on the buckling characteristics of circular cylinders are investigated. The first problem deals with the effect of linearly varying axial compressive stress, such as would be produced by the weight of the propellant in a solid-propellant engine case. The results indicate that the ratio of the maximum critical compressive stress induced by the shear load to the critical uniform compressive stress varies from 1.9 for the curvature parameter z equal to 1.6 as z becomes infinite. In particular, the increase in stress is less than 20 per sq. Ft. For z greater than 100. The stability of thin cylinders loaded by lateral external pressure varying linearly in the longitudinal direction is also investigated. The results indicate that for z greater than 100, the buckling coefficients are proportional to square root Z.","title":"The buckling of cylindrical shells under longitudinally varying loads.","url":"cran.html#doc1173"},
{"description":"Lu ting and paul A. Libby Polytechnic institute of brooklyn, and general applied science laboratories, inc. In connection with a study of the wakes behind bodies in hypersonic flow carried out for the missile and space vehicle division of the general electric company, it was desired to estimate the eddy viscosity in axisymmetric, compressible wakes. Because of the lack of applicable experimental data, it was found necessary to make such an estimate by rationally extending the few available data for incompressible flows to the compressible case. This suggested the application and extension of the transformations applied to turbulent boundary layers in reference infinitesimal mass are invariant with transformation, mager showed that the partial differential equations for the compressible turbulent boundary layer can be transformed to incompressible form. The validity of this assumption and of the transformations was established for several boundary-layer flows by comparison with experiment.","title":"Remarks on the eddy viscosity in compressible mixing flows.","url":"cran.html#doc17"},
{"description":"Yashura, M. J. Ae. Scs. 29, 1962, 667. Axisymmetric viscous flow past unyawed very slender bodies of revolution is treated within the category of the perfect gas. Attention is paid especially to the effect of transverse curvature of the body. From the transformed equations, the similarity conditions are deduced, and the parameter characterizing the effect of transverse curvature is obtained. Several numerical solutions of similarity equations for hypersonic flows are presented, and upon the basis of these results, the effect of the transverse-curvature parameter is discussed. A method of applying the local-similarity approximation to obtain the approximate solution for nonsimilar cases is described, as are practical applications to incompressible flow past a long cylinder and to hypersonic flow past a very slender cone. Comparison with experimental results shows fair agreement with calculations using the local-similarity approximation in the present range of experimental flow conditions.","url":"cran.html#doc494","title":"Axisymmetric viscous flow plast very slender bodies of revolution."},
{"description":"Landahl, M.T. Kth aero. T.N.40, 1954. When certain conditions are fulfilled for thickness ratio, aspect ratio, and reduced frequency for a three-dimensional wing, it can be shown that the partial differential equation for the non-steady perturbation potential can be reduced to a comparatively simple linear equation. The solution is then obtained by applying a fourier transformation in the free-stream direction and then using an iterative process developed by adams and sears for steady flow. The method gives solutions valid for low combinations of aspect ratio and reduced frequency. The method is applied to a delta wing oscillating in some selected rigid and elastic modes. From the results it can be seen that the special non-steady forces in the potential equation, which are neglected in slender-body theory, are very important. Stability derivatives can also be obtained by the method and it is seen that the damping in pitch may be negative at m 1 for delta wings of too high aspect ratio.","url":"cran.html#doc916","title":"The flow around oscillating low aspect ratio wings at transonic speeds."},
{"description":"Reeder, J.P. Nasa tn.d735, 1961. All of the vtol research aircraft discussed in this paper have successfully demonstrated conversion from hovering to airplane flight and vice versa. However, control about one or more axes of these aircraft has been inadequate in hovering flight. Furthermore, ground interference effects have been severe in some cases and have accentuated the inadequacy of control in hovering and very low speed flight. Stalling of wing surfaces has resulted in limitations in level-flight deceleration and in descent, particularly for the tilt-wing aircraft, which in this case is a very rudimentary type. Minor modifications to the wing leading edge have, however, produced surprisingly large and encouraging reductions in adverse stall effects. Height control in hovering and in low-speed flight has proved to be a problem for the aircraft not having direct control of the pitch of the rotors. The other systems have shown undesirable time lags in development of a thrust change.","url":"cran.html#doc1169","title":"Hangling qualities experience with several vtol research aircraft."},
{"title":"Newtonian flow over a surface.","url":"cran.html#doc1304","description":"Giraud, J.P. Colston symposium on hypersonic flow, bristol, 1959. A general method is presented for the study of a three-dimensional hypersonic flow about a body of arbitrary shape when. The manner of constructing a double asymptotic development in and is shown. Formulae are given which enable the first three terms of this development to be obtained while neglecting. The theory is then applied to the case of a body of circular-cone shape. The pressure is given as a triple development in accordance with the preceding parameters and the angle of attack,. This development neglects. A. Ferri's vortical layer is brought into evidence. A second application is devoted to calculation of the total forces acting upon bodies of revolution at angles of incidence, while neglecting. General formulae are established for the coefficients of axial force, normal force and moments. The formulae are developed according to the powers of incidence, the first terms of each formula being of very simple form."},
{"url":"cran.html#doc1295","title":"Recent advances in nonequilibrium dissociating gasdynamics.","description":"Li, T.Y. Ars jnl. 1961. The purpose of this paper is to review some recent advances in the study of gasdynamic problems including effects of chemical reactions. To provide a background for the study the general concepts shall be outlined briefly. The discussions of the recent developments are restricted to inviscid flow problems only, neglecting viscosity, heat conduction and diffusion. Particular attention is directed to recent advances in analyses of nonequilibrium dissociating gas flows. In the hypersonic flight regime, high stagnation enthalpies sufficient to cause dissociation are realized. When the time to reach equilibrium is comparable with the time it takes for a fluid particle to pass through the flow, then there exist regions of the flow field where nonequilibrium states are encountered. A brief survey of both the linear and the nonlinear methods of treatment of these nonequilibrium flows, including some new developments that have not appeared elsewhere, will be presented."},
{"url":"cran.html#doc247","title":"The calculation of the pressure distribution on thick wings of small aspect ratio at zero lift in subsonic flow.","description":"Weber, J. Arc r + m 2993. The method of expressing the velocity increment over aerofoils directly in terms of the section ordinates wings of finite aspect ratio. The wings considered are untapered in plan-form but may be tapered in thickness. The section can be of any given shape so that in this sense the analysis is more general than that of refs. 3 to 6 which deal with wings of biconvex section. The coefficients required in the calculation are tabulated for the centre-section of straight and swept-back wings of aspect ratios 0.5,. 1,. 2,. And 4, the wing of infinite aspect ratio having been treated in ref. 1. The remaining calculations can be made very quickly. Since wings of very small aspect ratio can be treated also by the method of slender-body theory, the relations between linear theory, slender-body theory, and linearised slender-body theory are discussed. For the special case of ellipsoids, the results obtained from the various methods are compared with the exact solution."},
{"url":"cran.html#doc904","title":"Calibration of the standard pitot-static head used in the rae low speed wind tunnels.","description":"Kettle, D.J. Rae tech.memo 222, 1951. Recent results of tests in the R.A.E. Wind tunnels concerned with the measurement of pressure distributions have shown slight discrepancies between the readings of various static pressure tubes and calculated pressure distributions. As a consequence some doubt was felt concerning the calibrations of tunnel static pressure and upon the validity of the reading given by the standard pitot-static head. It was therefore decided to check the standard pitot-static head used in the R.A.E. Wind tunnels, against an instrument similar to the measurements of static pressure were also made using a long tube where the interference from head and support is calculated to be small. This note gives the results of tests made in the 5 ft open jet wind tunnel and the no. 1 11 ft wind tunnel in order to determine the necessary correction to the reading of static pressure given by the R.A.E. Pitot-static head. The tests were made during september and october, 1951."},
{"url":"cran.html#doc713","title":"Static longitudinal stability characteristics of a blunted glider re-entry configuration having 79.5degree sweepback and 45degree dihedral at a mach number of 6.2 and angles of attack up to 20degree.","description":"Mayo, E.E. Nasa tm x-222. 1959. 5degree sweepback and 45degree dihedral at a mach number of 6.2 and angles of attack up to 20degree. An experimental investigation was conducted at a mach number of 6.2 to determine the static longitudinal stability characteristics of a model of a blunted glider reentry configuration having 79.5degree sweepback and 45degree dihedral. The free-stream reynolds number for the investigation was 3.0 x 10 based on the basic model length of 7.5 inches. Tests were made through an angle-of-attack range from 0degrees to investigation showed that incorporating 10degree nose incidence in the basic model resulted in a lower lift-curve slope, a lower lift-drag ratio, a higher value of trim lift coefficient, and a decrease in static longitudinal stability. In comparison, the effect of extending the configuration length and incorporating 10degrees and 20degrees boattail angles resulted in smaller changes in the longitudinal stability characteristics of the model."},
{"url":"cran.html#doc554","title":"Generalized heat transfer formulas and graphs.","description":"Detra, R.W. And Kidalgo, H. Ars J. 1961. Utilizing the research results of previously reported investigations of the laminar, turbulent and radiative heat transfer in dissociated air, some generalized formulas for calculating heat transfer are given. Graphs for determining the laminar heat transfer, momentum thickness reynolds number, and turbulent heat transfer distributions around an axisymmetric body are also given. These heat transfer correlations are valid for velocities between 6000 and 26, 000 fps and for altitudes up to 250, 000 ft. This range of velocities and altitudes covers the important re-entry regime of practical re-entry trajectories having interest today. In the last section of this report these generalized results are specialized for icbm nose cone re-entry applications. These formulas and graphs may be found useful for making rapid engineering estimates and preliminary design evaluations of the heating problems associated with re-entry into earth's atmosphere."},
{"url":"cran.html#doc52","title":"Procedure for calculating flutter at high supersonic speed including camber deflections, and comparison with experimental results.","description":"Morgan, H.G. Naca tn.4335, 1958. A method which may be used at high supersonic mach numbers is described for calculating the flutter speed of wings having camber in their deflection modes. The normal coupled vibration modes of the wing are used to derive the equations of motion. Chord deflections of the vibration modes are approximated by polynomials. The wing may have a control surface and may carry external stores although no aerodynamic forces on the stores are presented. The aerodynamic forces that are assumed to be acting on the wing are obtained from piston theory and also from a quasi-steady form of a theory for two-dimensional steady flow. Airfoil shape and thickness effects are taken account of in the analysis. The method is used to calculate the flutter speed of some wings which had been previously tested at mach numbers of 1.3 to 3.0. Comparison of the calculations and experiment is made for flat-plate 60 and 45 delta wings and also for an untapered 45 sweptback wing."},
{"description":"Tao, L.N. J. Ae. Scs. 1960, 334. This paper is concerned with the problem of the formation of couette flow--I.E., the problem of how the velocity profile varies with the time tending asymptotically to that of the steady flow of an electrically conducting viscous fluid in the presence of a magnetic field. The governing equations and boundary conditions are established and discussed. The cases of both vanishing and nonvanishing mean induced electric field strengths are solved in terms of complimentary error functions as well as some elementary functions. It is shown that the solutions are reducible to that of the steady case as the time approaches infinity, and to that of the nonmagnetic field as the hartmann number becomes zero. Some numerical calculations are given. The results indicate that in the presence of a magnetic field the flow rate is reduced depending on the magnitude of the hartmann number, and that the magnetic field /assists/ the flow to reach its steady condition.","title":"Magnetohydrodynamic effects on the formation of couette, flow.","url":"cran.html#doc1273"},
{"url":"cran.html#doc580","title":"New thermo-mechanical reciprocity relations with application to thermal stress analysis.","description":"Biot, M.A. J. Ae. Scs. 26, 1959. Based on the variational formulation of linear thermodynamics as developed previously by the writer, thermomechanical reciprocity relations are discussed which lead to new methods of analysis of thermal stresses. These reciprocity relations are quite different from the usual ones derived from the analogy of thermal loading with a combination of surface and body-force distribution. The results are applicable to stationary and transient temperatures in elastic and viscoelastic structures. The methods are entirely variational and do not require the evaluation of the temperature field. The stresses at one point are expressed directly in terms of any arbitrary distribution temperatures applied externally, including the effect of surface heat-transfer layer. The concepts and procedures are illustrated on a simple example. The relation is pointed out between the reciprocity property and the generalization of castigliano's principle to thermomechanics."},
{"title":"An approximate solution of the compressible laminar boundary layer on a flat plate.","url":"cran.html#doc611","description":"Monaghan, R.J. Rae tn. Aero.2025. Following a major assumption that enthalpy and velocity are dependent only on local conditions, an enthalpy-velocity relation is obtained for the laminar boundary layer on a flat plate where subscripts p refer to the plate, 1 to the free stream and e to the equilibrium temperature condition at the plate. When compared with general results, this relation (exact for prandtl number o = 1) gives a close approximation to crocco's numerical results for o = 0.725 and 1.25, up to. Using the above relation in conjunction with the approximate viscosity-temperature relation suggested by chapman and rubesin, and with young's suggested first approximation for shearing stress it is shown that close approximations to displacement thickness and velocity distribution are given by and where and which serves to define C. These have the advantage of being algebraic in form whereas previous results have involved complex numerical integrations for individual cases."},
{"title":"Subsonic aerodynamic flutter derivatives for wings and control surfaces, /compressible and incompressible flow/.","url":"cran.html#doc748","description":"Minhinnick, I. T. R.A.E. Rep. Structs. 87. July 1950. This report gives tables of the two-dimensional subsonic flutter derivatives,. Where possible the values given are based on the published work of various authors, but some have been specially calculated for this report. Wing derivatives are given for mach numbers 0, 0.5, 0.6 and 0.7 for the frequency parameter range 0 /0.04/ 0.2 /0.2/ 1.6 and mach numbers 0 and 0.7 for frequency parameter 5.0. Control surface derivatives are given for mach numbers 0 and 0.7 for control surface/ wing chord ratios 0.02 /0.02/ 0.10 /0.05/ 0.50 and frequency parameters are also given for mach numbers 0, 0.5, 0.6 and 0.7 for frequency parameter 0 /0.04/ 0.2 /0.2/ 1.4. Control surface-tab derivatives are given for some particular values of the variables and methods of obtaining approximate values of these derivatives for other values of the variables are suggested. Control surface and tab derivatives are in all cases for no aerodynamic balance."},
{"title":"Elastic stability of circular cylindrical shells stabilized by a soft elastic core.","url":"cran.html#doc1172","description":"Goree, W.S. And Nash, W.A. Exp. Mech. 2, 1962. The effect of a soft elastic core upon the buckling strength of a thin, circular, cylindrical shell is investigated experimentally. Two types of loading are considered.. (a) axial compression, and (b) uniform radial-band loading, where the width of the band is small compared to the length of the shell. For each type of loading it is shown that the strengthening effect of the elastic core becomes more significant with the increasing values of the radius-thickness ratio. For example, it is shown that for the geometric and elastic constants considered it is possible, with the presence of the core, to increase the axial buckling stress by as much as 65 percent over the values found for those without an elastic core. The elastic core is even more effective in stabilizing the shell against buckling due to band loading, the peak pressure required to buckle the filled specimen being 7.30 times that required to buckle the unfilled shell."},
{"description":"Culick, F.E. And Hill, J. J. Ae. Scs. 25, 1958. The stewartson-illingworth transformation is applied to the integral momentum equation for compressible boundary-layer flow, leaving the x-coordinate transformation unspecified, however. It is shown that the transformed equation is the integral momentum equation for incompressible flow if (a) the effect of compressibility on the boundary-layer shape parameter h can be represented by and (b) the x-coordinate transformation is chosen to be suitably related to the ratio of skin-friction coefficients in compressible and incompressible flows. Experimental evidence is presented which shows that condition (a) is satisfied for turbulent boundary layers up to m = 5. An x-transformation is chosen according to (b) and an equation is presented which gives the turbulent boundary-layer growth in compressible flow in terms of a simple quadrature. The predictions of this equation are then compared with some measurements on wind-tunnel nozzles.","url":"cran.html#doc377","title":"A turbulent analog of the stewartson-illingworth transformation."},
{"url":"cran.html#doc1098","title":"An experimental investigation of ablating material at low and high enthalpy potentials.","description":"Rashis, B. And Walton, T.E. Nasa tm.x-263, 1960. The ablation performance characteristics of a number of materials were derived from tests conducted in a mach number 2.0 ethylene-heated high-temperature air jet having a maximum stagnation enthalpy potential of approximately 1, 200 btu lb. The tests were conducted with 6- inch-diameter blunt nose shapes. The surface of most of the materials after testing was generally smooth and the unablated portions of the specimens were in appearance the same as before testing. In all cases, the back or inside surface of the specimens exhibited no evidence of heating. An evaluation of the enthalpy potential effect was obtained by comparison of the present data with previous tests conducted, on the in a subsonic arc-heated air jet. The stagnation enthalpy potential of this facility was approximately 7, 000 btu lb. For teflon, the effective heat of ablation increased from approximately 1, 250 btu lb to enthalpy potential was increased from"},
{"title":"Numerical comparison between exact and approximate theories of hypersonic inviscid flow past slender blunt nosed bodies.","url":"cran.html#doc556","description":"Feldman, S. Ars J. 30, 1960. This paper presents numerical results of exact calculations of the inviscid equilibrium flow about a long hemisphere-cylinder in motion at hypersonic velocity. A comparison is made with blast wave as well as free layer theories of hypersonic flow. As a result of the comparison, it is concluded that the second-order blast wave theory can be used for the purpose of finding the shock shape and the body pressure distribution. However, this procedure is definitely empirical and cannot be justified on rational or theoretical grounds. We show that the presently calculated radial distribution of energy is radically different than that given by blast wave theory. If body shapes other than those considered here are of interest, the only reliable approach at the present time is to carry out numerical calculations. It was found that for certain flight velocities the pressure on the body does not decay to free stream pressure monotonically but overexpands."},
{"description":"Gersten, K. Agard R.299, 1959. The three-dimensional incompressible flow of fluid along the corner of two semi-infinite plates intersecting at right angles, especially the interference of the boundary layers of the two plates, is discussed. Mainly, the more important case of turbulent boundary layer is treated by means of experimental studies carried out at the technical university of braunschweig. Some theoretical results for laminar flow are also taken into account. In order to describe the interference effects in the boundary layer, an interference displacement thickness and an interference skin friction have been introduced. It is shown from experiments and also from theoretical considerations how these two quantities depend on reynolds number. Furthermore, the influence of interference on the transition from laminar to turbulent flow is investigated. In addition, some preliminary results are given about the effect of the pressure gradient on the interference effects.","url":"cran.html#doc610","title":"Corner interference effects."},
{"description":"Barmby, J.G. Naca R.1014, 1951. An experimental and analytical investigation of the flutter of sweptback cantilever wings is reported. The experiments employed groups of wings swept back by rotating and by shearing. The angle of sweep ranged from 0 to 60 and mach numbers extended to approximately 0.85. A theoretical analysis of the air forces on an oscillating swept wing of high length-chord ratio is developed, and the approximations inherent in the assumptions are discussed. Comparison with experiment indicates that the analysis developed in the present report is satisfactory for giving the main effects of sweep, at least for nearly uniform cantilever wings of high and moderate length-chord ratios. A separation of the effects of finite span and compressibility in their relation to sweep has not been made experimentally but some combined effects are given. A discussion of some of the experimental and theoretical trends is given with the aid of several tables and figures.","url":"cran.html#doc1337","title":"Study of effects of sweep on the flutter of cantilever wings."},
{"title":"The temperature history in a thick skin subjected to laminar heating during entry into the atmosphere.","url":"cran.html#doc982","description":"Sutton, G.W. Jet propulsion, vol. 28, january 1959, p 40-5 During high speed entry into the earth's atmosphere, a vehicle can be afforded thermal protection for the short period of entry heating by a thick outer skin, sometimes called a /heat sink/. The temperature distribution in such a heat sink has been found by integrating the product of the laminar aerodynamic heating rate and the appropriate green's function for a finite-thickness wall over the generalized trajectory for a vehicle entering the earth's atmosphere at high speeds dimensional heat conduction problem for laminar heating. The maximum surface temperature that occurs during the generalized entry trajectory for any combination of wall thickness and thermal properties is obtained from which the performance of any material can be found, provided that the average thermal properties may be used. As an example of the use of the solution, the performance of copper, graphite, molybdenum and tungsten are compared."},
{"description":"Olsson, C.O. And Orlik-ruckeman, K. Aero. Res. Inst. Sweden, R.52, 1954. An electronic apparatus for automatic evaluation of the damping of a harmonic oscillation has been designed and constructed. The apparatus is based on the idea of representing the harmonic damped oscillation by a rotating vector on the screen of a cathode-ray tube in such a way, that the rate of decrease of the length of the vector is a measure of the damping. The results are obtained simultaneously with the oscillation test as two numbers in decimal digits, which are inversely proportional to the logarithmic decrement and the frequency, respectively. The apparatus, which is named the /dampometer/, has been used for some time for free oscillation measurements of the dynamic stability derivatives of aeroplane models in windtunnels, and has proved to be very satisfactory. It gives results of usually higher accuracy than evaluation methods in common use, and permits a most considerable saving of time.","url":"cran.html#doc1113","title":"An electronic apparatus for automatic recording of the logarithmic decrement and frequency for oscillations in the audio and subaudio frequency range."},
{"description":"Revell, J.D. J. Ae. Scs.1960, 730. An analysis is made of the second-order effects of thickness on the unsteady aerodynamic forces on a slender pointed body of revolution in supersonic flow. The theory is restricted to harmonic oscillations for small angles of attack. The solution is obtained by approximating the nonlinear terms in the second-order potential equation by their first-order values and solving the resulting inhomogeneous partial differential equation, subject to more refined boundary conditions. The pressure equation is likewise refined and integrated to give the second-order corrections to lift and pitching moment coefficients. The analysis can be considered as an extension of the second-order, slender body theory of lighthill to the case of unsteady flow. The results indicate appreciable reductions in unsteady lift and damping moment coefficients when applied to slender cones. The present theory is estimated to be reliable provided that is less than 0.7.","url":"cran.html#doc1259","title":"Second-order theory for unsteady supersonic flow past slender pointed bodies of revolution."},
{"description":"Gerard, g and gilbert, A.C. J.app.mech. 24, 1957. This paper summarizes the optical and physical properties of the photoelastic model material paraplex p-43 over the temperature range from room temperature to -40 F. Descriptions are presented of techniques and equipment developed to obtain the modulus of elasticity, the material fringe value, and the thermal-expansion coefficient as a function of temperature. Experimental investigations were conducted into the plane-stress problems of a disk contracting upon an elastic inclusion and the transient thermal-stress field produced by a temperature differential suddenly applied to the upper edge of a long beam. The data are correlated with theory using the material properties obtained in the calibration phase. Also included are photographic results of an exploratory investigation of the thermal-shock phenomenon produced by the sudden application of a temperature differential upon plastic beams of various length-depth ratios.","title":"Photo-thermoelasticity.","url":"cran.html#doc462"},
{"title":"Thermodynamic coupling in boundary layers.","url":"cran.html#doc645","description":"Baron, J.R. Ars space flight rep. To the nation, 2206-61, 1961. Experimental results gathered in recent years for binary mixture mass transfer models are shown to yield consistent evidence of discrepancies with analytic considerations. Specifically, measured recovery temperatures are appreciably higher than those predicted ,. While heat transfer coefficients are satisfactorily reproduced. It is shown on the basis of both approximate and exact solutions for plates and stagnation points that the discrepancies in previous results are related to thermal diffusion effects, a major influence being apparent in application of the surface boundary condition for an adiabatic wall. As a result, some reexamination is necessary of past criteria for mass addition effects as they pertain to specific injected media. A prime example is the /equivalence/ of helium and air as coolants despite the heretofore suggested preference for low density injectants on a perfect gas basis. Ref. 16."},
{"url":"cran.html#doc497","title":"Theoretical and experimental investigation of thermal stresses in hypersonic aircraft wing structures.","description":"Tramposch, H. J. Ae. Scs. 29, 1962. A simple and relatively accurate analytic approximation is developed to determine the temperature and thermal-stress distribution in aircraft wing structures. Theoretical investigations show that the results of the existing thermal-stress theories which neglect the temperature gradient through the skin thickness may exceed, in the range of higher biot numbers, the true values by more than 30 percent. Refined photothermoelastic experiments verify these results and add another significant conclusion. They indicate that thermal stresses in wing structures generated by a variable heat-transfer coefficient coincide with the theoretical predictions which are based on a constant heat-transfer coefficient, as long as the latter represents the arithmetic average over the heating cycle and the variation is in the order of 10 percent. However, even much greater variations in the order of 100 percent produce only relatively small differences."},
{"description":"Gravalos, F.G., edelflet, I.H. And Emmons, H. 9th int. Astro. Fed. 1958. The supersonic flow about a blunt body of revolution for gases at chemical equilibrium. A method to determine the shock wave, and its location, about a body of revolution moving at supersonic speeds is given. The method provides also the means to compute the flow characteristics in the shock layer. The fluid in which the motion takes place is assumed to be in chemical equilibrium within the shock layer ,. Its thermochemical properties must be known. The essential new features of the method are.. A) it solves the direct problem, I. E., the initial data are the conditions upstream and the body shape ,. B) the integration of the fundamental equations is done in the physical plane and the difficulties inherent to other, less direct, mathematical formulations of the problem are avoided. A physical interpretation of the method is made which is in accord with the analytical definition of the problem.","url":"cran.html#doc410","title":"The supersonic flow about a blunt body of revolution for gases at chemical equilibrium."},
{"url":"cran.html#doc91","title":"Periodic temperature distribution in a two-layer composite slab.","description":"W. F. Campbell National aeronautical establishment, ottawa, ont., canada In a recent contribution to the reader's forum, under the above title, stonecypher outlined a method for finding the periodic temperature distribution in a two-layer composite slab, one exposed surface of the slab being insulated and the other subject to a sinusoidal temperature variation. Perfect thermal contact between the two layers, and constant thermal properties were assumed. Two years ago i drew attention in these pages to a method for determining the transient temperature in such a two-layer slab resulting from a triangular heat-input pulse. I should like to point out that this same method also is applicable to the case where one external face is given a sinusoidal temperature variation with time. The method is based on the analogy between one-dimensional heat flow and the flow of an electric current in a simple transmission line having only series resistance and parallel capacitance."},
{"description":"Yen, K.T. J. Ae. Scs. 1960, 607. This paper is concerned with the thrust generated by a jet flap. It is shown that a /linear/ thrust hypothesis can be obtained, provided linearized potential flow is assumed. In fact, the linearized problem of a jet-flap system is found to be the linear combination of a lift problem and a thrust problem. The lift problem gives all the lift generated, but it is of interest to note that the thrust problem would yield all the thrust developed by the jet flap within the limitation of the linearized theory. The mixing of the jet flap with the surrounding fluid is analyzed by the momentum-integral method. The analysis substantiates stratford's suggestion for obtaining an increase of thrust by causing the jet to mix with the main stream in a region of high suction. Finally, some approximate formulas, relating the thrust and the jet angle, are derived. The drag of the airfoil section and other viscous effects are, however, not considered.","url":"cran.html#doc1265","title":"On the thrust hypothesis for the jet flap including jet-mixing effects."},
{"description":"Rossow, V.J. Naca tn.2399, 1951. The analysis of technical note 2250, 1950, is extended to include the effects of flow rotation. It is found that the theoretical pressure distributions over ogive cylinders can be related by the hypersonic similarity rule with sufficient accuracy for most engineering purposes. The error introduced into pressure distributions and drag of ogive cylinders by ignoring the rotation term in the characteristic equations is investigated. It is found that the influence of the rotation term on pressure distribution and drag depends only upon the similarity parameter k (mach number divided by fineness ratio). Although the error in drag, due to neglect of the rotation term, is negligible at k=0.5, the error is about 30 percent at k=2.0. Charts are presented for the rapid determination of pressure distributions for rotational flow over ogive cylinders for all values of the similarity parameter between 0.5 and of mach number and fineness ratio.","title":"Applicability of the hypersonic similarity rule to pressure distributions which include the effects of rotation for bodies of revolution at zero angle of attack.","url":"cran.html#doc57"},
{"description":"Stewartson, K. J. Ae. Scs. 22, 1955, 303. The theory of the steady flow of a viscous compressible fluid past a flat plate at high mach number due to lees and probstein is extended by a more complete discussion of the flow in the inviscid layer between the shock wave and the boundary layer. It is shown that similar solutions exist in this layer, analogously to those found by li and nagamatsu in the boundary layer, and that the two may be joined to give, allowing one minor assumption, a full account of the flow. It is shown that the boundary-layer equations may be reduced to those for an incompressible fluid and that the von karman-pohlhausen method describes the flow in it with good accuracy. The tangent wedge approximation for the pressure on the plate, used by lees and his collaborators, is found to be in deficit by 10 per cent for air. Finally, it is shown that the theory for weak interaction cannot be extended further without a complete knowledge of the flow.","title":"On the motion of a flat plate at high speed in a viscous compressible fluid, ii, steady motion.","url":"cran.html#doc309"},
{"description":"Van driest, E.R. J.ae.scs. 18, 1951, 145. The continuity, momentum, and energy differential equations for turbulent flow of a compressible fluid are derived, and the apparent turbulent stresses and dissipation function are identified. A general formula for skin friction, including heat transfer to a flat plate, is developed for a thin turbulent boundary layer in compressible fluids with zero pressure gradient. Curves are presented giving skin-friction coefficients and heat-transfer coefficients for air for various wall-to-free-stream temperature ratios and free-stream mach numbers. In the special case when the boundary layer is insulated, this general formula yields skin-friction coefficients higher than those given by the von karman wall-property compressible-fluid formula but lower than those given by the von karman incompressible-fluid formula. Heat transfer from the boundary layer to the plate generally increases the friction and heat-transfer coefficients.","url":"cran.html#doc348","title":"Turbulent boundary layer in compressible fluids."},
{"description":"Lykoudis, P.S. J. Ae. Scs. 1961. The hypersonic flow of an electrically conducting fluid around the stagnation region of a sphere carrying a radial magnetic field is examined. By assuming a newtonian pressure distribution and constant density, the differential equation of the inviscid flow is integrated and a simple closed-form solution is obtained. It is found that the ratio of the stand-off distances of the shock wave for the magnetic and nonmagnetic cases does not depend explicitly on the magnetic parameter s (ratio of the ponderomotive force to the free-stream inertia force) nor on the density ratio (the value at the free stream divided by the value behind the shock wave) but on the product s at least for values of between and. The velocity gradient on the body is also calculated and the ratio of the magnetic to the nonmagnetic case is shown to depend on the parameter. The case of cylindrical shocks is also examined,. The same general conclusions are drawn.","title":"The newtonian approximation in magnetic hypersonic stagnation-point flow.","url":"cran.html#doc1238"},
{"description":"G. A. Allcock, A.M.I.E.E., A.M.brit.I.R.E. P. L. Tanner, M.sc. (eng), grad. I.E.E. K. R. Mclachlan, A.M.brit. I.R.E. A large proportion of the current research programme of the department of aeronautics and astronautics is concerned with the study of jet noise and boundary layer pressure fluctuations and their effect on aircraft structures. Early in the work it was decided that for a complete description of the random processes involved it would be necessary in the experimental programme to make correlation measurements in addition to the more standard spectrum and amplitude distribution measurements. It was also felt that it would be desirable from the university point of view to construct a general purpose correlator which could later be used on other types of work. To this end it was decided to give the correlator a wider bandwidth than might strictly have been necessary for the problems on hand. Subsequent development work has amply justified this decision.","title":"A general purpose analogue correlator for the analysis of random noise signals.","url":"cran.html#doc220"},
{"url":"cran.html#doc1329","title":"Some aspects of non-stationary airfoil theory and its practical application.","description":"Sears, W.R. J. Ae. Scs. 8, 1951, 104. This paper consists of three notes on the theory of two- dimensional thin airfoils in non-uniform motion.. Oscillating airfoil are collected from an earlier paper and are presented in convenient forms for practical application. Rigid airfoil passing through a vertical-gust pattern having a sinusoidal distribution of intensity. The lift is determined as a function of the reduced frequency (which in this case is proportional to the ratio of the airfoil chord and the wave length of the gust pattern) and is presented in the form of a vector diagram. It is shown that the lift acts at the quarter-chord point of the airfoil at all times. Calculation of the amplitude of torsional oscillation of a fan blade operating in the wake of a set of pre-rotation vanes. In a numerical example the amplitude is found to be small even when the vanes are spaced so that the exciting frequency coincides with the natural frequency of the fan blade."},
{"title":"Effects on adjacent surfaces from the firing of rocket jets.","url":"cran.html#doc697","description":"Bressette, W.E. And Leiss, A. Naca rm l 57d19a, 1957. This paper is a preliminary and brief account of some research currently being conducted to determine the jet effects on adjacent surfaces from the firing of rocket jets. Measurements of jet-effect pressures on a flat plate as well as shadowgraphs are presented that were obtained when a rocket jet at a mach number of 3 was exhausted downstream and upstream into free-stream flow at a mach number of 2 located from 2 to 4.7 rocket-jet-exit diameters from the plate. The jet effects on the flat plate with the rocket jet exhausting downstream are of the same order of magnitude as those previously obtained from sonic exits with a total pressure 10 times lower. A maximum pressure coefficient on the plate of rocket-jet-exit diameters below the plate, and an integration of the measured jet-effect pressures at this position resulted in a normal force on the plate equal to 2.3 times the thrust output of the rocket jet."},
{"description":"Turner, J.M. J. Ae. Scs. 1960. The method of direct formulation of the stiffness matrix is extended to include the effects of nonuniform heating and large deflections. The purpose is to develop an analytical tool for the treatment of actual structures. In the solution of aeroelastic problems the relations between forces and deflections must be determined. The usual stiffness matrix formulation of this relationship is limited to small temperature changes and small deflections. For large temperature changes additional terms are required. Also the problem becomes geometrically nonlinear when large deflections are involved. To overcome the inherent difficulties of the nonlinear problem for practical structures either an iterative or a step- by-step procedure must be used. The force-deformation relations necessary for this step-by-step or iterative approach are derived for an axially loaded member and for a plate element including the effects of thermal strains.","url":"cran.html#doc1361","title":"Large deflections of structures subjected to heating and external loads."},
{"url":"cran.html#doc35","title":"Stagnation point of a blunt body in hypersonic flow.","description":"Li, T.Y. And Geiger, R.E. J. Ae. Scs. 24, 1957, 25. The purpose of this paper is to present a method of calculation devised to yield all the important information on the symmetric inviscid hypersonic flow in the stagnation point region of a blunt body. The problem is the same as that considered by hayes who used a slightly different approach. It is demonstrated that hayes' results are valid in the stagnation point region and can hence be considered a basis for constructing less restricted solutions. Equations are presented giving velocity, pressure, detachment distance, and vorticity. The values of shock detachment distance and body pressure coefficient are compared with experimental data for spheres. The pressure comparison shows that the results of hayes and the theory presented herein represent a better approximation than the newtonian impact theory for hypersonic mach numbers. In conclusion, the possibility of refinements to this analysis is discussed."},
{"title":"Theoretical studies of unsteady transonic flow. Part iii. The oscillating low aspect ratio rectangular wing.","url":"cran.html#doc919","description":"Landahl, M.T. Aero. Res. Inst. Of sweden /F.F.A./ rep. 79, 1958. Part iii. The oscillating low aspect ratio rectangular wing. By expanding the velocity potential in an asymptotic series, the aerodynamic forces on an oscillating low aspect ratio rectangular wing are calculated. The approximate theory is valid for small values of ko /o semi-span-to-chord ratio,. K reduced frequency/ and complements an earlier low-aspect-ratio-wing theory by the author valid only for pointed wings like delta wings. The present report gives formulas for the calculation of generalized forces for any smooth, flexible or rigid mode of oscillation with spanwise symmetry. Comparisons with the slender-wing theory show that, except for wings of very low aspect ratio, unsteady-flow effects are appreciable even at fairly low reduced frequencies. Near the upper limit in ko for the applicability of the present theory good agreement is obtained with a recent theory for high aspect ratios."},
{"title":"Hypersonic strong viscous interaction on a flat plate with surface mass transfer.","url":"cran.html#doc305","description":"Li, T.Y. And Gross, J.F. Heat transfer and fluid mech. Inst. 1961, 146. The present report gives an account of the development of an approximate theory to the problem of hypersonic strong viscous interaction on a flat plate with mass-transfer at the plate surface. The disturbance flow region is divided into inviscid and viscous flow regions. The hypersonic small perturbation theory is applied to the solution of the inviscid flow region. The method of similar solutions of compressible laminar boundary layer equations is applied to the treatment of the viscous flow region. The law of surface mass-transfer for similar solutions is derived. The pressure and the normal velocity are matched between the inviscid and viscous flow solutions. Formulas for induced surface pressure, boundary layer thickness, skin friction coefficient, and heat transfer coefficient are obtained. Numerical results and their significance are discussed. Future improvements are indicated."},
{"description":"Leiss, A. And Bressette, W.E. Naca rm l56106, 1957. 80. As a continuation of previous research at mach numbers of 2.02 and 1.39, an experimental investigation was made of the pressures induced on a flat plate by a propulsive jet exhausting from sonic and supersonic nozzles at a free-stream mach number of 1.80. Measurements of the pressure distribution on a flat-plate wing were made at zero angle of attack for four different locations of the jet exhaust nozzle beneath the wing. Both a choked convergent nozzle and a convergent-divergent nozzle on the nacelle were used. The nozzles were operated at nacelle-exit total-pressure ratios from 2 to 16 and the reynolds number per foot was approximately 13 x 10. Two distinct shock waves impinged on the wing surface and greatly altered the pressure distribution at all nozzle positions. Positive incremental normal force resulted on the wing at all positions. Comparisons are presented for two free-stream mach numbers.","title":"Pressure distribution induced on a flat plate by a supersonic and sonic jet exhaust at a free-stream mach number of 1.80.","url":"cran.html#doc694"},
{"description":"Monaghan, R.J. Rae. Tn. Aero. 2407. This note gives formulae and approximations suitable for making preliminary estimates of aerodynamic heating rates in high speed flight. The formulae are based on the /intermediate enthalpy/ approximation which has given good agreement with theoretical and experimental evidence. In the general flight case they could be used in conjunction with an analogue computer or a step-by-step method of integration to predict the variations of heat flow and skin temperature with time. In the restricted case of flight at constant altitude and mach number, simple analytical methods and results are given which include the effects of radiation and can be applied to /thick/ as well as /thin/ skins where h is the aerodynamic heat transfer factor, and g, d and k are the heat capacity, thickness and thermal conductivity of the skin. If 0.1 the skin is approximately /thin/, I.E. Temperature gradients across its thickness may be neglected.","title":"Formulae and approximations for aerodynamic heating rates in high speed flight.","url":"cran.html#doc606"},
{"title":"A theoretical calculation of the laminar boundary layer around an elliptic cylinder and its comparison with experiment.","url":"cran.html#doc1384","description":"Millikan, C.B. J. Ae. Scs. 3, 1936, 91. The author, in conjunction with th. Von karman, has recently given a new method of approximate integration of the prandtl boundary layer equations, which was developed in order to treat cases in which separation of a laminar boundary layer might be expected. The method was developed because some doubt was felt as to the accuracy with which the well-known pohlhausen analysis would describe conditions in the neighborhood of such a separation point. Numerical calculations were carried out for certain cases involving theoretical simplifications, and very considerable discrepancies were found between the results of the new and pohlhausen methods. The method was also used in developing a theory for the maximum lift coefficient of certain classes of airfoils. This theory gave satisfactory agreement with experiment but no direct experimental check on the boundary layer analysis itself has been given up to the present."},
{"description":"Rogers, E.W.E. And Hall, I.M. A.R.C., C.P. 481, may 1959. Distributed roughness bands of no.320 and no.500 carborundum were found to be effective in causing boundary-layer transition if they extended over the first 5( and 10( respectively of the local chord. Use of larger grain sizes, or increases in the band width for a given grain size resulted in a drag penalty. With very large particle sizes /about between the particles. The drag penalty was constant over the test mach number range /0.80 to 1.15/ and decreased slowly with incidence. The wing lift and pitching moment were only slightly modified by the presence of any of the roughness bands tested, but this result would not of course necessarily apply to wings of other planforms or section shapes. The test reynolds number was about 2.7 million. In the appendix, the structure of the roughness bands is discussed, as well as the details of the materials used and the techniques used to apply the band.","url":"cran.html#doc796","title":"An investigation at transonic speeds of the performance of various distributed roughness bands used to cause boundary layer transition near the leading edge of a cropped delta half-wing."},
{"title":"An investigation of some aspects of the sonic boom by means of wind tunnel measurements of pressures about several bodies at a mach number of 2. 01.","url":"cran.html#doc808","description":"Carlson, H.W. Nasa tn.d161, 1959. 01. An investigation of some aspects of the sonic boom has been made with the aid of wind-tunnel measurements of the pressure distributions about bodies of various shapes. The tests were made in the langley at a mach number of 2.01 and at a reynolds number per foot of 2.5 x 10. Measurements of the pressure field were made at orifices in the surface of a boundary-layer bypass plate. The models which represented both fuselage and wing types of thickness distributions were small enough to allow measurements as far away as 8 body lengths or 64 chords. The results are compared with estimates made using existing theory. To the first order, the boom-producing pressure rise across the bow shock is dependent on the longitudinal development of body area and not on local details. Nonaxisymmetrical shapes may be replaced by equivalent bodies of revolution to obtain satisfactory theoretical estimates of the far-field pressures."},
{"description":"Gregory, N. And Walker, W.S. Pt. 1, arc r + m 2779, 1950. The effect of isolated surface excrescences in a laminar boundary layer in producing disturbances which may lead to turbulent flow has been examined experimentally by several methods. Photographs of some of the flow patterns visualised by smoke and china-clay techniques are given. The critical heights of pimple which just give rise to spreading wedges of turbulent flow have been measured on a flat plate and on two aerofoils at several angles of incidence. The results are analysed and are presented in a form which enables approximate estimates to be made of the protuberances permissible on laminar-flow surfaces at full-scale flight reynolds numbers. The estimates suggest that at an altitude of 30, 000 ft the critical pimple height is 0.004 in. For a speed of 350 M.P.H., whilst 0.002 in. May be permissible at all subsonic speeds. At sea-level, however, the tolerances are approximately halved.","url":"cran.html#doc1324","title":"The effect on transition of isolated surface excrescences in the boundary layer."},
{"description":"Denison, M.R. And Baum, E. Aiaa jnl. 1, 1963, 342. The momentum equation was uncoupled from the other conservation equations for the case of a finite initial profile in a laminar free shear layer. The equation was solved numerically, in the crocco coordinate system, using an implicit finite difference method. Profiles of velocity and shear function were obtained as a function of streamwise distance. The initial profiles as the flow separates from the rear of the body correspond to the blasius profile in transformed coordinates. For large distances downstream, the profiles approach the chapman distribution, corresponding to the case of zero initial free shear layer thickness. The effect of these results on calculations of base pressure and wake angle is discussed. A method for the calculation of finite chemical kinetic effects on the profiles of temperature and chemical composition in the free shear layer with finite initial thickness is outlined.","url":"cran.html#doc943","title":"Compressible free shear layer with finite initial thickness."},
{"url":"cran.html#doc729","title":"Stresses in continuous skin stiffener panels under random loading.","description":"Lin, Y.K. J. Aero. Sc. January 1962. Theoretical aspects involved in the prediction of stress levels for continuous skin-stiffener panels subjected to a random pressure field are considered in the light of powell's general theory for statistical superposition of modal response. The choice of structural model is dictated by the prevalence of skin-stiffener construction in modern flight vehicle design. The present study clearly demonstrates that any truly adequate prediction of stress levels in actual aircraft structures requires a much better representation of structural characteristics than can be provided by single panel idealizations. In an example considering fuselage panels exposed to jet engine noise, essential agreement is shown with experimental data, although better correlation is shown for rms stress than for power spectrum. It is shown that reduction of stress level by increasing damping is effective only in the higher frequency range."},
{"description":"O'bryan, T.C. Nasa tn.d977, 1961. Dynamic-pressure measurement, in ground effect, have been obtained about a single-rotor helicopter and a dual-propeller vtol aircraft. The results indicate that the slipstream dynamic pressure along the ground, some distance from the center of rotation, is not a function of disk loading but merely a function of the gross weight or thrust of the aircraft. Furthermore, for a given gross weight the thickness of this outward flowing sheet of air is less for a small-diameter propeller (higher disk loading propeller). The variation of the dynamic-pressure flow field for single and dual propellers or rotors is significantly different in the plane of symmetry between the two rotors than in a direction normal to this plane. The interaction of the two flows produces a region of upflow in this plane where the fuselage is located, and the decay of the maximum dynamic pressure with distance ahead of the fuselage is slower.","url":"cran.html#doc1165","title":"An investigation of the effect of downwash from a vtol aircraft and a helicopter in the ground environment."},
{"url":"cran.html#doc16","title":"Transformation of the compressible turbulent boundary layer.","description":"Mager, A. J. Ae. Scs. 25, 1958, 305. The transformation of the compressible turbulent boundary- layer equations to their incompressible equivalent is demonstrated analytically. The transformation is essentially the same as that for the laminar layer, first given by stewartson, except that the explicit relation between the viscosity and temperature is not required. A key point in the analysis is the modification of the stream function to include a mean of the fluctuating components and the postulate that the apparent turbulent shear, associated with an elemental mass, remains invariant in the transformation. The values of the incompressible friction coefficients and of pressure rise causing separation thus transformed show good agreement with the experimentally measured and independently reported results. An application of the transformation to the self-preserving boundary layers and to the computations of general boundary-layer flow is shown."},
{"title":"Calculation of potential flow about bodies of revolution having axes perpendicular to the free-stream direction.","url":"cran.html#doc498","description":"Hess, J.L. J. Ae. Scs. 29, 1962. A general method is described for calculating, with the aid of an electronic computer, the potential flow about arbitrary bodies of revolution whose axes are perpendicular to the free-stream direction. When combined with the solution for the axisymmetric flow about these bodies, this method makes it possible to calculate the pressure distribution on any body of revolution at angle of attack forward of any separated region of the flow, and also to calculate the flow at points off the body surface. After the basic equations of the method have been derived, its accuracy is exhibited by comparison with analytic solutions for ellipsoids of revolution. Calculated pressure distributions are then compared with experimental data for a variety of bodies. The agreement is quite satisfactory in all cases. The calculated velocities for other selected bodies are presented to exhibit certain properties of this type of flow."},
{"description":"Letko, W. Nasa memo 1-18-159l, 1959. 11 of the lift, drag and pitching moment characteristics of a number of blunt low-fineness-ratio bodies. A number of blunt bodies having shapes that may be suitable for atmospheric reentry were tested to determine the lift, drag, and pitching-moment characteristics at a mach number of 3.11 and a reynolds number of 6 x 10 based on maximum body diameter of 2 inches. The results of the tests showed that all the bodies were statically stable about a point located one-third of the body length from the nose. The results also showed that high-drag bodies which have a large portion of their afterbodies negatively sloped (decrease in cross-sectional area from nose to base) may have a negative lift-curve slope. This negative slope results from the large negative lift component of the axial force obtained with those bodies and the fact that with negatively sloped afterbodies only small normal forces are developed.","title":"Experimental investigation at a mach number of 3. 11 of the lift, drag and pitching moment characteristics of a number of blunt low-fineness-ratio bodies.","url":"cran.html#doc816"},
{"description":"Hartree, D.R. Proc. Cam. Phil. S. 33, 1937, 223. The differential analyser has been used to evaluate solutions of the equation y''' = -yy'' + with boundary conditions y = y' = 0 at x = 0, as which occurs in falkner and skan's approximate treatment of the laminar boundary layer (see abstract 1081 (1932)). A numerical iterative method has been used to improve the accuracy of the solutions, and the results show that the accuracy of the machine solutions is about insufficient to specify a unique solution for negative values of,. A discussion of this situation is given, and it is shown that for the application to be made of the solution the appropriate condition is that from below, and as rapidly as possible, as. The condition that from below can be satisfied only for values of greater than a limiting value whose value is approximately -0.199, and which is related to the point at which the laminar boundary layer breaks away from the boundary.","title":"On an equation occurring in falkner and skan's approximate treatment of the equation of the boundary layer.","url":"cran.html#doc479"},
{"description":"Yasuhara, M. J. Phys. Soc. Japan, 12, 1957, 177. The hypersonic viscous flow past a flat plate with suction or injection is dealt with by karman-pohlhausen's method in special cases when suction or injection velocity proportional to, especially for the region of strong interaction between the shock wave and the boundary layer, were p is the pressure on the plate and x is the distance measured along the plate from its leading edge. Several numerical examples are given, which shows similar effects of injection to those in the case of incompressible flow that the injection makes all the height of the shock wave, the thickness of the boundary layer and the pressure on the plate larger than those in the case of no injection. On the contrary, in the case of suction no remarkable change both in the height of the shock wave and the pressure on the plate can be seen and only the velocity profile in the boundary layer is affected by the suction.","title":"On the hypersonic viscous flow past a flat plate with suction or injection.","url":"cran.html#doc308"},
{"description":"Mccune, J.E. And Resler, E.L. J. Ae. Scs. 27, 1960. The effects of compressibility on the steady motion of a highly conducting fluid past thin cylindrical bodies in the presence of a magnetic field are studied. Procedures are developed for the solution of this class of magnetoaerodynamic problems over the entire mach number range and for all ratios of magnetic to fluid-dynamic pressure. The results obtained are analogous either to the ackeret theory or the prandtl-glauert rule of conventional aerodynamics, depending on the relative values of the flow speed and the appropriate speed of propagation of magnetoacoustic disturbances. The methods used and the physical interpretation of the solutions obtained vary according to the orientation of the magnetic field with respect to the flow direction. The results of the theory are explained in terms of the anisotropic propagation of magnetoacoustic pulses studied previously by several authors.","url":"cran.html#doc297","title":"Compressibility effects in magneto-aerodynamic flows past thin bodies."},
{"title":"On the propagation and structure of the blast wave.","url":"cran.html#doc1327","description":"Sakurai, A. J. Phys. Soc. Japan, 8, 1953, 662. Concerning blast waves with front surfaces of plane, cylindrical and spherical shape, the propagation velocity u and the distribution of hydrodynamical quantities are discussed. The solutions are constructed in the form of power series in (c u), where c is the sound velocity of undisturbed fluid. Especially r, the distance of shock front from the charge, is represented as, where r is the characteristic length related to the energy of explosion, j and are constants, and a=0, 1, 2 correspond to plane, cylindrical and spherical case, respectively. In this paper the first approximations for a=0, 1 are discussed (the case a=2 has been discussed by G. I. Taylor). The solution is obtained numerically for the case of the adiabatic index. The approximate solution is also considered. Using these solutions, is found to be. The second approximation will appear in part 2 to be published subsequently."},
{"description":"Janos, J.J. Nasa tn d-649, march 1961. 0. Measurements were made of loads induced on a flat-plate wing by an air jet exhausting perpendicularly through the wing and normal to the free-stream flow. The investigation was conducted at a free-stream mach number of 2.0 and a reynolds number per foot of 14.4 x 10. An axially symmetric sonic nozzle and two supersonic nozzles were employed for the jets. The supersonic nozzles consisted of an axially symmetric nozzle with exit mach number of 3.44 and a two-dimensional nozzle with exit mach number of 1.76. The ratio of nozzle total pressure to free-stream static pressure was varied from 20 to 110. Negative loads were induced on the flat-plate wing by all the jets. As the nozzle pressure ratio was increased the magnitude of interference loads due to jet thrust decreased. The chordwise center-of-pressure location generally moved toward the nozzle center line as the pressure ratio was increased.","url":"cran.html#doc970","title":"Loads induced on a flat plate wing by an air jet exhausting perpendicularly through the wing and normal to a free-stream flow of mach number 2.0."},
{"description":"Stewartson, K. Q.app.math. 13, 1955, 113. In this paper the incompressible boundary layer over a circular cylinder in an axial flow is investigated far from the leading edge. If u and v are the velocity components in the x and r direction respectively and a stream function is introduced by and, then for a constant free-stream velocity has the following asymptotic form.. Where the p's are determined successively, first for s=1 and all t, then s=2 and all t, etc., from ordinary differential equations. Here and log c=euler's constant. It is shown that the effect of the curvature of the body (in planes perpendicular to the flow) is to increase the skin friction. Also the case in which the free-stream velocity is proportional to (at the method breaks down), is studied. It is concluded that the effect of the curvature of the cylinder, when the boundary layer has a thickness comparable with its radius of curvature, is to delay separation.","url":"cran.html#doc105","title":"The asymptotic boundary layer on a circular cylinder in axial incompressible flow."},
{"description":"Schjeldrup, H.C. Air eng. 1959. With the introduction of high-powered propulsion systems, and paralleling their continued development, an accompanying increase in acoustical problems has arisen. Of these acoustical problems, that of acoustical fatigue failures has become paramount in the eyes of the structural engineer. Aircraft designed to normal strength requirements have been known literally to fall apart under acoustical loading. This problem has required much endeavour to produce a solution, and considerable structural research, based upon results of siren or other testing, have proved inadequate. This failure to find a satisfactory solution has resulted in the conviction that the final proof of a design can be found only in proof testing. Proof testing, in the acoustic fatigue sense, is the testing of a design structure in a simulated acoustical environment for a period of time long enough to assure equality with design life.","url":"cran.html#doc724","title":"Structural acoustic proof testing."},
{"description":"Molyneux, W.G. Rae tn.struct.294, 1961. An investigation is made of the parameters to be satisfied for thermo-aeroelastic similarity. It is concluded that complete similarity obtains only when aircraft and model are identical in all respects, including size. By limiting consideration to conduction effects, by assuming the major load carrying parts of the structure are in regions where the flow is either entirely laminar, or entirely turbulent, and by assuming a specific relationship between reynolds number and nusselt number, an approach to similarity can be achieved for small scale models. Experimental and analytical work is required to check on the validity of these assumptions. It appears that existing hot wind tunnels will not be completely adequate for thermo-aeroelastic work, and accordingly a possible layout for the type of tunnel required is described. Automatic programmed control of the tunnel would appear to be necessary.","title":"Scale models for thermo-aeroelastic research.","url":"cran.html#doc184"},
{"description":"Newton, J.F. And Spaid, F.W. Ars jnl. 32, 1962, 1203. Tests were conducted with 1300- to 1500-lb thrust solid rocket motors in order to investigate the side-force generation mechanisms associated with the injection of a secondary fluid into the expansion cone of a solid propellant rocket nozzle for thrust-vector control. The nozzles were 15 conicals with a nominal expansion ratio of. All firings were conducted in zero-flow ejectors. Freon-12, water, and gascous nitrogen were used as the injectant. Nozzle-wall pressure profiles, side thrust, and the nozzle-wall shock interface were recorded. The general character of the pressure disturbance was defined. The major portion of the side force was generated by the pressure disturbance downstream of the injector. The axial-thrust augmentation generated by the injectant was calculated. The effects of nozzle-expansion ratio and injector location on the side force were clearly illustrated.","title":"Interaction of secondary injectants and rocket exhaust for thrust vector control.","url":"cran.html#doc1326"},
{"url":"cran.html#doc964","title":"On the theory of discharge coefficients for round entrance flowmeters and venturis.","description":"Rivas, M.A. And Shapiro, A.H. Trans. A.S.M.E., V. 78, april 1956, pp 489-497. A theory of rounded-entrance flowmeters, based on a consideration of the potential and boundary-layer flows in a converging nozzle, is constructed. Curves are presented showing the discharge coefficient as a function of diameter reynolds number, with the /total equivalent length tional length-diameter ratio of the contraction section of the asme long-radius nozzle is presented. The theoretical curves of discharge coefficient versus diameter reynolds number are in good agreement with experiment over a range of reynolds number from 1 to 10. The theory provides a rational framework for correlating and extrapolating experimental results,. It shows the effects of contraction shape and location of pressure taps,. It furnishes values of discharge coefficient for untested designs,. And It suggests precautions to be taken in design, installation, and operation."},
{"description":"Mazelsky, B. And Drischler, J.A. Naca tn 2739, 1952. 5 and 0.6. The indicial lift and moment functions are determined approximately for sinking and pitching motion at mach numbers m of 0.5 and 0.6. These functions are determined from a knowledge of the existing oscillatory coefficients at the low reduced frequencies and from approximate expressions of these coefficients at the high reduced frequencies. The beginning portion of the indicial lift function associated with an airfoil penetrating a sharp-edge gust in subsonic flow is evaluated by use of an exact method. By use of an approximate method for determining the remaining portion, the complete indicial gust function is determined for m 0.5, m 0.6, and m 0.7. All the indicial lift and moment functions are approximated by an exponential series,. The coefficients which appear in the exponential approximations for each indicial function are tabulated for m 0.5, m 0.6, and m 0.7.","url":"cran.html#doc702","title":"Numerical determination of indical lift and moment functions for a two dimensional sinking and pitching airfoil at mach numbers 0.5 and 0.6."},
{"title":"On the flow of a sonic stream past an airfoil surface.","url":"cran.html#doc39","description":"Sinnott, C.S. J.ae.scs. 26, 1959, 169. This study of the flow about an airfoil in a near-sonic stream indicates the important factors determining the pressure distribution on the airfoil. Analysis of the mach wave pattern suggests that the supersonic domain of the flow can be derived from two simple-wave flows, one arising from the mach waves reflected at the sonic line and the other from the changes in airfoil surface slope. The compressive effect of the reflected mach waves is determined quantitatively as a function of airfoil leading-edge geometry from an analysis of measured pressure distributions for uncambered airfoils,. And It is shown how this can be superimposed on the wave system from the curved surface to give an equivalent simple-wave flow over the airfoil. An application of this scheme to the calculation of the pressure distribution over an airfoil in a sonic stream gives results in good agreement with experiment."},
{"description":"Michielsen, H.F. Advances in astronautical science, vol 4 plenum press 1959. Pp 255-310 The rate of decay of elliptic satellite orbits, due to atmospheric drag, is investigated through variation of parameters and through use of an atmospheric model involving a power function between density and altitude. This model is shown to fit actual conditions better than an exponential function. The effects of the equatorial belt and the rotation of the earth are investigated. The conclusion is reached that through these anomalies atmospheric drag substantially affects the orbit elements, especially those defining the orbit plane. An alternate approach of variation of parameters is presented, by which a direct relation between period decay and instantaneous density conditions is established. This approach, by itself specifically adequate for prediction work, also opens an avenue for systematic and unified evaluation of observed decay.","title":"Orbit decay and prediction of the motion of artificial satellites.","url":"cran.html#doc618"},
{"title":"Experiments on axi-symmetric boundary layers along a long cylinder in incompressible flow.","url":"cran.html#doc261","description":"Yashura, M. Trans. Japan soc.ae.sc. 2, 1959. Experiments on axi-symmetric boundary layers along a long cylinder were made especially to investigate the effect of transverse curvature on the velocity profile. Laminar velocity profiles were measured and compared with theoretical ones with good accuracy. A representative profile was plotted to see the effect of transverse curvature, which showed small, but obvious effect accompanied by increasing skin friction. The transition of the flow from laminar to turbulent was observed, and its reynolds number was estimated to occur at 1.2 1.8x10 in the present experiment. The turbulent profile was also measured and plotted by using the coordinates to express the wall law deduced by richmond, from which it was estimated that, as the ratio of the momentum thickness to body radius increases, the profile near the outer layer tends to bend down relative to the line of logarithmic wall law."},
{"title":"An investigation of separated flows, part ii: flow in the cavity and heat transfer.","url":"cran.html#doc45","description":"Charwat, A.F. J. Ae. Scs. 28, 1961, 513. The first portion of this paper describes studies of the internal structure of the separated flow in a notch at a free-stream mach number of 3. Observations include.. Flow visualization, spark- schlieren pictures of the fluctuations of the free shear layer, and studies of the diffusion of heat from sources placed in the separated region. The second part describes measurements of local heat transfer to the wall. The external mach number, the length-to-depth ratio of the cavity, the ratio of the oncoming boundary layer thickness to the notch depth (in the turbulent flow region), the thermal to-momentum thickness ratio of the boundary layer and, finally, the geometry of the internal boundary of the separated region are varied as systematically as possible. On the basis of these observations, a simple model of the flow in and the heat transfer across the separated region is formulated."},
{"description":"Yates, J.E. And Zeydel, E.F.E. Aiaa jnl. 1, 1963, 350. The present paper derives generalized aerodynamic forces for slender supersonic aircraft on the basis of slender-body theory. Particular consideration is given to configurations which are spanwise flexible. To treat configurations with flexible wings and bodies, the slender wing-body problem is first reduced to a simple body problem whose solution is well known, and a solution of the latter is obtained, utilizing the circle theorem or method of images and a known solution of the airfoil equation for a double interval. With this approach, it is not necessary to apply conformal mapping techniques, and the solution so obtained is valid for arbitrary spanwise downwash distributions. On the basis of slender-body theory, the velocity potential and, subsequently, the generalized aerodynamic forces are derived for a general class of spanwise flexible wing-body configurations.","title":"Unsteady aerodynamic forces on slender supersonic aircraft with flexible wings and bodies.","url":"cran.html#doc1197"},
{"title":"The unsteady lift of a wing of finite aspect ratio.","url":"cran.html#doc698","description":"Jones, R.T. 1940, naca rep. 681. Unsteady-lift functions for wings of finite aspect ratio have been calculated by correcting the aerodynamic inertia and the angle of attack of the infinite wing. The calculations are based on the operational method. The starting lift of the finite wing is found to be only slightly less than that of the infinite wing,. Whereas the final lift may be considerably less. The theory indicates that the initial distribution of lift is similar to the final distribution. Curves showing the variation of lift after a sudden unit change in angle of attack, during penetration of a sharpedge gust, and during a continuous oscillation are given. Operational equivalents of these functions have been devised to facilitate the calculation of lift under various conditions of motion. As an application of these formulas, the vertical acceleration of a loaded wing caused by penetrating a gust has been calculated."},
{"title":"Investigation of the effects of ground proximity and propeller position on the effectiveness of a wing with large chord slotted flaps in redirecting propeller slipstream downward for vertical take-off.","url":"cran.html#doc1094","description":"Kuhn, R.E. Naca tn.3629, 1956. An investigation of the effects of ground proximity and propeller position on the effectiveness of a wing equipped with large-chord slotted flaps in redirecting the slipstreams from large-diameter propellers downward for vertical take-off has been conducted in a static-thrust facility at the langley aeronautical laboratory. The results indicate that, with the propeller thrust axis on the wing chord plane, both the angle through which the slipstream is deflected and the ratio of resultant force to thrust are reduced as the ground is approached. At positions nearest the ground some of the loss in resultant force is regained. Lowering the thrust axis below the wing chord plane reduces the adverse effects of the ground and also reduces the large diving moments associated with the slotted-flap arrangement. The static-thrust efficiency of the propellers is slightly reduced by the ground effect."},
{"description":"Nielsen, J.N. And Kaattari, G.E. Naca til.2950. The modified slender-body method used by nielsen, katzen, and tang in rm a50f06, 1950, to predict the lift and moment interference of triangular wing-body combinations has been adapted to combinations with other than triangular wings. That part of the method for predicting the effect of the body on the wing has been retained, but a new method for predicting the effect of the wing on the body has been presented. These methods have been applied to the prediction of the lift-curve slopes of nearly 100 triangular, rectangular, and trapezoidal wing-body configurations. The estimated and experimental values for the lift-curve slopes agree for most of the cases within 10 percent. Some of the higher-order effects that must be taken into account in a theory that is to give greater accuracy than the present one are discussed. A numerical example illustrating the method is included.","title":"Methods for estimating lift interference of wing-body combinations at supersonic speeds.","url":"cran.html#doc923"},
{"url":"cran.html#doc1017","title":"Note on creep buckling of columns.","description":"Gerard, G. J. Ae. Scs. 19, 1962, 714. It appears from librove's interesting analysis that, for the case of creep buckling of columns, the initial imperfections contained in ordinary columns provide the mechanism by which failure due to creep occurs after a period of time. In fact, it can be concluded from this analysis that a theoretically perfect column that is initially loaded below the time-independent critical load will not buckle at all. This is an interesting contrast to the case of static buckling where small initial imperfections play an insignificant role, since the failing load of an initially imperfect column is substantially the same as that of a theoretically perfect column. It is of interest, therefore, to conjecture whether there is any possible mechanism by which a column containing no initial imperfections can fail as a result of creep when the initial load is less than the theoretical buckling load."},
{"description":"Van hise, V. Nasa r78, 1960. A systematic study of induced pressures on a series of bodies of revolution with varying nose bluntness has been made by using the method of characteristics for a perfect gas. The fluid mediums investigated were air and helium and the mach number range was from 5 to 40. A study of representative shock shapes was also made. Flow parameters obtained from the blast-wave analogy gave good correlations of induced pressures and shock shapes. The induced-pressure correlations yielded empirical equations for air and helium which cover the complete range of nose bluntness considered. (nose fineness ratios varied from 0.4 to 4.) available experimental results were in good agreement with the characteristics solutions. Properties connected with the concept of hypersonic similitude enabled correlations of the calculations to be made with respect to nose shape, mach number, and ratio of specific heats.","title":"Analytic study of induced pressure on long bodies of revolution with varying nose bluntness at hypersonic speeds.","url":"cran.html#doc421"},
{"description":"Rainey, A.G. Naca R.1305, 1957. The oscillating air forces on a two-dimensional wing oscillating in pitch about the midchord have been measured at various mean angles of attack and at mach numbers of 0.35 and 0.7. The magnitudes of normal-force and pitching-moment coefficients were much higher at high angles of attack than at low angles of attack for some conditions. Large regions of negative damping in pitch were found, and it was shown that the effect of increasing the mach number from 0.35 to 0.7 was to decrease the initial angle of attack at which negative damping occurred. Measurements of the aerodynamic damping of a 10- percent-thick and of a 3-percent-thick finite-span wing oscillating in the first bending mode indicate no regions of negative damping for this type of motion over the range of variables covered. The damping measured at high angles of attack was generally larger than that at low angles of attack.","title":"Measurements of aerodynamic forces for various mean angles of attack on an airfoil oscillating in pitch and on two finite-span wings oscillating in bending with emphasis on damping in the stall.","url":"cran.html#doc1115"},
{"description":"Klebanoff, P.S. J. Ae. Scs. 22, 1955, 803. In his study of the effect of roughness on transition, H. L. Dryden found, on the basis of available data, that the effect of a two-dimensional roughness element such as a /trip wire/ could be represented reasonably well in terms of a functional relation between and, where is the reynolds number of transition based on distance from the leading edge, is the height of the roughness element, and is the boundary-layer displacement thickness at the position of the element. At his suggestion some additional data were obtained, primarily to extend the range to higher values of, during the course of an investigation of transition on a flat plate conducted at the national bureau of standards. After the results on the two- dimensional roughness elements were obtained, it appeared to be desirable to see whether a row of three-dimensional roughness elements would behave in the same way.","title":"Measurements of the effect of two-dimensional and three-dimensional roughness elements on boundary layer transition.","url":"cran.html#doc8"},
{"url":"cran.html#doc1057","title":"The uniform section disk spring.","description":"Almen, J.O. And Laszlo, A. Asme trans. 58, 1936, 305. The authors point out in this paper that initially coned annular-disk springs of uniform cross section may be proportioned to give a wide variety of load-deflection curves not readily obtainable with the more conventional forms of springs, and that, although the versatility of this type spring has long been indicated, the formulas available have not been presented in a manner to disclose readily the effect of spring proportions on characteristics. Therefore the authors have derived the formulas presented in this paper with the intention that the formulas will aid the designer in arriving at suitable characteristics by choice of spring geometry. These new formulas have been in use for several years at the general motors corporation research laboratories section, and their reliability has been checked by tests of springs used in a variety of special test equipment."},
{"url":"cran.html#doc754","title":"Heat transfer through laminar boundary layers on semi-infinite cylinders of arbitrary cross section.","description":"Bourne, D.E. And Wardle, S. J. Ae. Scs. 29, 1962, 460. This paper shows how to calculate the rate of heat transfer through a laminar boundary layer on a semi-infinite cylinder of arbitrary cross section. The cylinder is placed in a stream of incompressible fluid, the flow at infinity being parallel to the generators, and is maintained at a uniform temperature. A series solution for small downstream distances and an asymptotic formula for large downstream distances are given. To cover the intermediate range an approximate pohlhausen solution is obtained,. A correction of the error involved in the pohlhausen solution is suggested which, it is believed, will lead to final errors of at most 2 percent. The calculations are applied to elliptic cylinders, and illustrate the effect on the local rate of heat transfer of varying the ratio of the major and minor axes of cross section, the length of perimeter being held fixed."},
{"title":"A study of the simulation of flow with free stream mach number 1 in a choked wind tunnel.","url":"cran.html#doc1153","description":"Spreiter, J.R., smith, D.W. And Hyett, B.J. Nasa tr r-73, 1960. The degree to which experimental results obtained under choking conditions in a wind tunnel with solid walls simulate those associated with an unbounded flow with free-stream mach number 1 is investigated for the cases of two-dimensional and axisymmetric flows. It is found that a close resemblance does indeed exist in the vicinity of the body, and that the results obtained in this way are generally at least as accurate as those obtained in a transonic wind tunnel with partly open test section. Some of the results indicate, however, that substantial interference effects, particularly those of the wave reflection type, may be encountered under certain conditions, both in choked wind tunnels and in transonic wind tunnels, and that the reduction of these interference effects to acceptable limits may require the use of models of unusually small size."},
{"description":"Lundgen, T.S., atabeck, B.H. And Chang, C.C. Phys. Fluids 4, 1961, 1006. Parallel flow of an electrically conducting viscous incompressible fluid in a rectangular duct with transverse magnetic field is considered. The walls of the duct which are parallel and perpendicular to the imposed magnetic field are taken to be nonconducting and perfectly conducting, respectively. Assuming the fluid to be at rest at the initial moment, exact solutions for the velocity and magnetic field components are obtained in the form of convolution integrals taking the longitudinal pressure gradient as an arbitrary given function of time. Later, taking a step function for the pressure gradient, these expressions are integrated. For this case, the effect of the strength of the imposed magnetic field on the development behavior of the flow is studied. It is found that except for very large magnetic fields, the flows are over damped.","title":"Transient magnetohydrodynamic duct flow.","url":"cran.html#doc653"},
{"url":"cran.html#doc227","title":"A technique for improving the predictions of linearised theory on the drag of straight edge wings.","description":"Randall, D.G. Arc cp394, 1957. The curve of drag against mach number for straight-edged wings, calculated by using the linearised theory of supersonic flow, displays discontinuities in slope at the various mach numbers for which the edges are sonic. These features, which are not observed in practice, are due to the fact that linearised theory predicts an infinite pressure along a subsonic or sonic edge. It is shown that if the linearised equation of supersonic flow is used to determine the flow over straight-edged wings, but the linearised boundary condition is replaced by the full placed by plausible values. On this basis a simple method is derived for improving the linearised predictions of the drag of straight-edged wings which exhibits satisfactory agreement with experimental results. While the technique is not directly applicable to ridge lines, an artifice renders them amenable to similar treatment."},
{"url":"cran.html#doc1362","title":"Non-linear analysis of heated, cambered wings by the matrix force method.","description":"Warner lansing, irving W. Jones, paul ratner Grumman aircraft engineering corporation Various extensions of the matrix force method for complex structure analysis are presented and illustrated with the objective of expanding its range to handle the problems likely to be encountered in advanced vehicle wing design. Methods are covered in detail for (1) determining the change in flexibility that occurs when thermal stresses are present, and also how large these stresses must be to cause buckling, (2) including the non-linear effect of large deflections by an iterative procedure, and (3) analyzing a wing that is initially slightly cambered and warped with either or both of the aforementioned effects present. Formulas are given for calculating the input matrix terms as are the matrix equations and supporting theoretical discussion. An example illustrates the nature and magnitude of the effects being examined."},
{"url":"cran.html#doc785","title":"The flow of fluid along cylinders.","description":"Cooke, J.C. Quart. J. Mech. App. Math, vol.x /3/, 1957, P. 312-321. The boundary layer equations for uniform flow parallel to the generators of any cylinder without corners are put into the form of a series of linear third-order differential equations. The first three of these are the same as those obtained by seban and bond /1/ for a circular cylinder and solved by kelly /2/. The rest have additional terms depending on the radius of curvature of the cylinder and its derivatives. The problem is also attacked by a pohlhausen method as far as four terms of the series. For large distances from the front, rayleigh's method, as given by hasimoto /3/, gives the first two terms of an asymptotic expansion for the drag. Explicit calculations are made of the drag of an elliptic cylinder of eccentricity 1/2 3. There is evidence that the drag is everywhere less than that of a circular cylinder of the same perimeter."},
{"title":"On the ground level disturbance from large aircraft flying at supersonic speeds.","url":"cran.html#doc253","description":"Lilley, G.M. And Spillman, J.J. Coa n103. The whitham-walkden theory for the estimation of the strength of shock waves at ground level from aircraft flying at supersonic speeds is applied to the case of a typical projected supersonic civil transport aeroplane. If a figure of 2 lb sq.ft. (including a factor of 2 for ground reflection) is taken as an upper limit for the acceptable strength of the bow wave from such an aircraft it is shown that restrictions on the climb and flight plan will be involved. The advantage of the employment of larger engines with or without afterburning is discussed, with reference also to the penalties involved owing to the increase in weight of the aircraft and its direct operating costs. Finally it is suggested that an aircraft of given volume could be designed, by suitable choice of thickness and lift distribution, to minimise the strength of the shock waves in the far field."},
{"description":"Seide, P. J. App. Mech. 24, 1957, 547. Equations, somewhat more accurate than those recently presented by N. J. Hoff, are derived for bending and buckling of thin circular conical shells under arbitrary loading. These equations reduce to donnell's equations for thin cylindrical shells when the cone semivertex angle becomes very small and the minimum radius of curvature of the median surface approaches a constant value. At the other end of the scale the equations reduce to the well-known equations for flat circular plates when the cone semivertex angle approaches a right angle. In addition, for the entire range of cone semivertex angles the equations reduce to the known equations for axisymmetrical bending when variations of the displacements around the circumference vanish. The problem of bending is reduced to the solution of a single fourth-order partial differential equation with variable coefficients.","url":"cran.html#doc936","title":"A donnell-type theory for asymmetrical bending and buckling of thin conical shells."},
{"description":"Rogers, E.W.E. And Hall, I.M. A.R.C., C.P. 510, september 1959. Tests have been made in three N.P.L. Wind tunnels on a pressure-plotting model consisting of a long cylinder with a hemispherical nose. The surface pressure distributions were measured for stream mach numbers between 0.7 and 1.1 at zero model incidence, and schlieren photographs were taken. The blockage ratios were 0.211(, 0.117( and 0.120(. The principal feature of the flow is the effect of working section size on the rate at which the terminal shock wave moves back along the model with increasing stream mach number. This is thought to depend mainly on the distance from the model to the slotted walls of the tunnel, and not necessarily on the blockage ratio. The distance of the solid sidewall is important in influencing the local mach number ahead of the terminal shock, by reflecting the expansion-wave system originating near the model nose.","url":"cran.html#doc800","title":"Wall interference at transonic speeds on a hemisphere cylinder model."},
{"url":"cran.html#doc881","title":"Cumulative damage in fatigue.","description":"Miner, M.A. J. App. Mech. 12, 1945, a159. The phenomenon of cumulative damage under repeated loads was assumed to be related to the net work absorbed by a specimen. The number of loading cycles applied expressed as a percentage of the number to failure at a given stress level would be the proportion of useful life expended. When the total damage, as defined by this concept, reached 100 per cent, the fatigue specimen should fail. Experimental verification of this concept for an aluminum alloy, using different types of specimens, various stress ratios, and various combinations of loading cycles is presented. These data are also analyzed to provide information on different stress ratios when an s-n curve for any one ratio is known. Results of a sample analysis based on experiments are given. It is concluded that a simple and conservative analysis is possible using the concept of cumulative fatigue damage."},
{"url":"cran.html#doc245","title":"The ground effect on the jet flap in two dimensions.","description":"Huggett, D.J. Arc 19, 713, 1957. This paper presents the results of the first part of an experimental investigation of the ground effect on simple jet flap aerofoils. In this part of the work an aerofoil having a 58.1 deg jet flap was tested under two-dimensional conditions. The pressure lift on the aerofoil was measured, with the ground at fixed positions, for varying jet momentum coefficients. It was found that the effect of the ground on the pressure lift was very small up to a certain critical jet coefficient. On increasing the jet coefficient beyond the critical value a marked loss of pressure lift was observed. This critical value referred to is approximately the same as the jet coefficient at which the jet first hits the ground. Some significant, though highly tentative comments, are made regarding the practical application of this work to the take-off characteristics of a jet flapped aircraft."},
{"url":"cran.html#doc148","title":"On displacement thickness.","description":"Lighthill, M.J. J.fluid mech. 4, 1958, 383. Four alternative theoretical treatments of 'displacement thickness', and, generally, of the influence of boundary layers and wakes on the flow outside them, are set out, first for two-dimensional, and then for three-dimensional, laminar or turbulent, incompressible flow. They may be called the methods of 'flow reduction', 'equivalent sources', 'velocity comparison' and the principal expression obtained for the displacement thickness in three-dimensional flow may be written if, as orthogonal coordinates (x, y) specifying position on the surface, we choose x as the velocity potential of the external flow, and y as a coordinate, constant along the external-flow streamlines, such that h dy is the distance between (x, y) and z is the distance from the surface, u and v are the x and y components of velocity, and u takes the value u just outside the boundary layer."},
{"url":"cran.html#doc338","title":"Mass transfer cooling at mach number 4. 8.","description":"Leadon, B.M., scott, C.J. And Anderson, G.E. J. Ae. Scs. 25, 1958. 8. Mass-transfer experiments on a 5 mil wire porous cone of 20 total angle have been conducted at using air and helium injection. Details of the experimental technique are described in references 1 and 2. In the laminar boundary layer the recovery factors and heat-transfer coefficients measured with zero injection agreed within per cent with theory. Transition reynolds numbers observed on the porous cone with zero injection were half as large as observed on a smooth, impermeable model of identical geometry in the same channel, but injection of large amounts of air or helium did not cause transition to move forward from its zero-injection position on the porous cone. Distributed roughness of this type apparently does not disturb impermeable wall theory, but it masks whatever effective roughness may be caused by discrete pore injection."},
{"title":"Magnetohydrodynamic free-convection pipe flow.","url":"cran.html#doc88","description":"Cramer, K.R. J. Ae. Scs. 28, 1961, 736. It has been shown that transverse magnetic fields of practical strengths exert considerable influence on liquid-metal, free-convection, vertical, flat-plate and parallel-plate flow fields. The extent of influence was determined by the magnitude of a nondimensional parameter a which is the ratio of the hartmann number to the fourth root of the grashof number, and is a measure of the relative influence of the magnetic and buoyant forces. In this note the steady, fully developed, laminar, free-convection flow of a fluid of electrical conductivity through a fully submerged, open-ended, constant-temperature, vertical pipe located in a transverse magnetic field of strength is analyzed in terms of the same parameter. The magnitude of its influence on the velocity and temperature profiles, the surface shear and heat transfer, and the volumetric flow rate is determined."},
{"description":"Van driest, E.R. Naca tn.2597, 1952. In the present investigation of the flow of air in a thin laminar boundary layer on a flat plate, the crocco method has been used to solve the simultaneous differential equations of momentum and energy involved in such flow. The crocco method was used because it gave accurate results for arbitrary prandtl number near unity. The prandtl number was taken at 0.75, the specific heat was held constant, and the sutherland law of viscosity-temperature variation was assumed to represent the viscosity data starting with an initial ambient temperature of -67.6 F. The main results presented here are the skin-friction and heat-transfer coefficients as functions of reynolds number, mach number, and wall-to-free-stream temperature ratio. Variations of shear, velocity, temperature, and mach number across the boundary layer are included. The crocco method is discussed in detail.","url":"cran.html#doc50","title":"Investigation of laminar boundary layer in compressible fluids using the crocco method."},
{"description":"Grimminger, G., williams, E. P., and young, G. J. Aero. Sc. V. 17, november, 1950. The importance of body lift lies in the fact that at moderate angles of attack and high mach number it can constitute an appreciable part of the total lift of a winged missile. In this paper an attempt has been made to analyze body lift in hypersonic flow by an approximate method and, together with a correlation of existing experimental data, to indicate the probable variation of body lift over a wide range of mach numbers extending from low supersonic to hypersonic. The method of analysis of hypersonic flow over inclined bodies of revolution employed herein has been denoted as the hypersonic approximation. It is an improvement on the newtonian corpuscular theory of aerodynamics, since it considers the centrifugal forces resulting from the curved paths of the air particles in addition to the impact /newtonian/ forces.","title":"Lift on inclined bodies of revolution in hypersonic flow.","url":"cran.html#doc360"},
{"description":"Barry, F.W., shapiro, A.H. And Neumann, E.P. J. Ae. Scs. 18, 1951, 229. The development of supersonic compressors, supersonic diffusers, and high-speed aircraft points to the increasing importance of the interaction between shock waves and boundary layers. The experimental work reported here is intended to (1) provide a better understanding of the nature of the shock boundary-layer interaction, (2) serve as a guide and stimulus to theoretical work, and (3) develop an empirical method for predicting the effects of the interaction. Experiments were performed on the reflection of an oblique shock from a boundary layer on a flat surface at a mach number of 2.05. The effects of shock strength and boundary-layer regime were explored. The results are in the form of schlieren photographs, constant-density contours found from interferometer photographs, and static pressure distributions at the plate surface.","title":"The interaction of shock waves with boundary layer on a flat surface.","url":"cran.html#doc345"},
{"description":"Culick, F.E.C. Aiaa jnl. 1963, 783. An integral method previously used successfully in several kinds of boundary layer problems has been extended to treat simultaneous heat and mass transfer in a binary-mixture laminar boundary layer when the pressure is uniform. The principal results are two pairs of dual integral relations arising from solutions to the integral concentration and energy equations. One pair connects the surface mass transfer rate and surface concentration of injected gas,. The other relates surface temperature and heat transfer rate in the presence of mass transfer. Only the cases of helium and air injection into an undissociated air stream are discussed in detail, but the method can be applied to problems involving other gases. The approximate results agree quite well with some numerical solutions and with recent experimental results for which no numerical solutions are available.","url":"cran.html#doc1185","title":"An integral method for calculating heat and mass transfer in laminar boundary layers."},
{"title":"Influence coefficients for real gases.","url":"cran.html#doc583","description":"Mario william cardullo U.S. Naval air rocket test station, lake denmark, dover, N.J. In the analysis of one-dimensional fluid-flow problems, it is often assumed that the behavior of the medium is that of a perfect gas. This assumption is justified, provided the pressure and temperature range of interest is small and near atmospheric. At higher pressures and temperatures various deviations are introduced thereby causing deviations from the results obtained by using the ideal fluid-flow equations. In this note, influence coefficients, similar to those developed by shapiro, are presented for the case of real gases. This analysis is based upon the use of various functions of the compressibility factor emmons. Some of the assumptions made were as follows.. (1) the flow is one-dimensional and steady, (2) changes in the stream properties are continuous, and (3) the flow is comprised of imperfect gases"},
{"description":"Romano, F. And Kempner, J. Pibal R.415, 1958. This paper presents an analysis of the deflections of and stresses in a short noncircular cylindrical shell of uniform wall thickness whose median-surface cross section is described analytically by a simple expression corresponding to a family of doubly symmetric ovals. The cylinder is under a uniform lateral load and is simply supported at its edges. The small deflection analysis considered is based upon a series solution of appropriate differential equations of shell theory which leads ultimately to infinite sets of algebraic equations, truncated forms of which are considered. Numerical values of the significant stresses and displacements for points of the oval cylinder, which are 5 percent of the axial length and 2.5 percent of the circumferential length apart, have been calculated for an oval cross section with a major-minor axis ratio of 1.10.","url":"cran.html#doc852","title":"Stress and displacement analysis of simply supported non- circular cylindrical shell under lateral pressure."},
{"url":"cran.html#doc630","title":"Stagnation region in rarefied high mach number flow.","description":"Cheng, H.K. And Chang, A.L. A.I.A.A. J. 1963, 231. Paper describes results of numerical solution of the viscous shock-layer equations for axisymmetric stagnation region, using the viscosity-temperature law with w=0.65, pr=0.71 and y=1.25. Purpose is to establish applicability of the simple approximation of w=1 (obtained earlier) to air at low reynolds numbers and low ratios of wall temperature to stagnation temperature. Using a reference temperature (closely equal to eckert's) to interpret the linear results, excellent agreement is found, in the limit of, over a wide range of reynolds numbers, covering fully merged shock layers as well as boundary layers with and without vorticity interaction. Agreement with recent experiments of ferri et al is as good as to be expected from shock-layer approximation. Paper provides valuable extension of the applicability of the reference temperature concept."},
{"url":"cran.html#doc60","title":"Estimation forces and moments due to rolling for several slender tail configurations at supersonic speeds.","description":"Bobbitt, P.J. And Malvestuto, F.S. Naca tn.2955, 1953. The velocity potentials, span loadings, and corresponding force and moment derivatives have been theoretically evaluated for a number of slender-tail arrangements performing a steady rolling motion at supersonic speeds. The method of analysis is based upon an application of conformal-transformation techniques. The utilization of these techniques allows the simple determination of the complex potentials for various types of two-dimensional boundary-value problems. In addition, two simple and often-used approximations to the rolling derivatives have been compared with the corresponding exact values determined by the method presented in this report. In order to show the importance of wing-tail interference, the effect of the flow field behind a rolling wing on the tail characteristics has been illustrated for a simple wing-tail arrangement."},
{"url":"cran.html#doc523","title":"Approximate determination of position of the sonic line for a blunt body in hypersonic flow.","description":"Rahman, M.A. J. Ae. Scs. 29, 1962. The detached shock in front of a blunt body in hypersonic flow tends to acquire the shape of the frontal curvature of the body. Thus the curvature of the shock can be assumed to be the same as that of the body, at least up to the sonic point (point a, fig. 1). If the equation of curvature of the body is known, the equation of curvature of the shock is also known. In this paper, with this assumption, a method is described to determine the approximate position of the sonic line (ao'b, fig. 1). The shock-detachment distance is assumed known. The method is, of course, general. This can be applied to any detached shock provided its equation of curvature is known corresponding to that of the body. For simplicity the detached shock is assumed to be circular in this paper and the procedure is outlined below with the assumption that the sonic line ao'b is parabolic."},
{"description":"Rattayya, J.V. J. Ae. Scs. 20, 1962, 534. The flutter problem of flat circular panels with edges elastically restrained against rotation has been formulated in terms of small-deflection plate theory. The panel is subjected to uniform all-round tension or compression in its middle plane, in addition to the supersonic compressible flow passing over its upper surface with still air below. Linear piston theory is employed to predict the aerodynamic load on the vibrating panel. The problem is investigated by a rayleigh-type analysis involving chosen modes of the panel as degrees of freedom. In order to investigate the convergence of the solution, the flutter-mode shape of the clamped-edge panel has been expressed in a series form in powers of r cos O. The results of three-, four-, and five-term approximations have displayed oscillatory behavior with apparently rapid convergence of the solution.","url":"cran.html#doc627","title":"Flutter analysis of circular panels."},
{"description":"Chu, C.K. And Lynn, Y.M. Aiaa jnl. This paper presents a study of the steady two-dimensional magnetohydrodynamic flow of an infinitely conducting fluid past a nonconducting wedge with nonaligned flow and magnetic field. The flows considered are in the /superfast/ or fully hyperbolic regime. The flows consist of several regions of uniformity connected by shocks and expansion waves. Because of the boundary condition on the magnetic field, the magnetic field must be the same in the regions above and below the wedge,. Thus the flows in these regions are coupled, unlike in the case of ordinary supersonic gasdynamics. Only small wedge angles and weak waves (characteristics) are considered. The problem thus is linearized, and explicit solutions are obtained which are qualitatively similar to the nonlinear solutions. Some interesting and unexpected features arise, and they are discussed in detail.","url":"cran.html#doc1181","title":"Steady magnetohydrodynamic flow past a non-conducting wedge."},
{"description":"Thwaites, B. Aero. Quart. 1, 1949-1950. After analyzing a large class of boundary-layer velocity-profiles, the author discovered that the functions l(m) and h(m) for all such cases differ only slightly from each other over the whole range of positive and negative pressure gradients. Here l, m and h are defined by being the velocity-component in the x direction and u the value of u at the edge of the boundary-layer and and the displacement and momentum thickness, respectively. Based on this discovery, an approximate method is proposed by constructing two universal curves l(m) and h(m) for all conceivable boundary-layer flows found in practice. Once these are chosen, karman's momentum-integral can be written in the form, v being the kinematic viscosity coefficient, and can be integrated numerically. As examples, both howarth's and hartree's tained is considered good for practical purposes.","title":"Approximate calculation of the laminar boundary layer.","url":"cran.html#doc1365"},
{"url":"cran.html#doc371","title":"Note on tip-bluntness effects in the supersonic and hypersonic regimes.","description":"Bennett, F.D. J. Ae. Scs. 24, 1957, 314. In a recent letter, M. H. Bertram presents some data on flows at m = 6.85 around 10 half-angle cones with blunted tips. Since the demarcation between the supersonic and hypersonic regimes is not sharp and since one expects hypersonic flows to be generally similar to those at lower mach numbers-- especially where viscous effects do not predominate throughout the entire field of interest--it is of some value to compare bertram's results with those obtained by giese and bergdolt for 15 half-angle cones at m = 2.45. Following the observation by charters and stein that drag coefficient measurements on blunted cones imply a reynolds number effect, giese and bergdolt study the convergence to conical flow of the perturbed flow about a cone with truncated tip. They employ the mach-zehnder interferometer and the conical flow criterion as analytical tools."},
{"url":"cran.html#doc118","title":"The transonic flow of a compressible fluid through an axially symmetrical nozzle.","description":"Tomotika, S. And Hasimoto, Z. J.math.phys. 29, 1950, 105. By a method similar to that developed by S. Tomotika and K. Tamada (quart. Appl. Math. 7, 381-397 (1950),. These rev. 11, 275) for computing two-dimensional mixed isentropic flows in the sonic region, the flow in the vicinity of the throat of an axially symmetrical nozzle is studied. Several exact solutions to von karman's equation for axially symmetrical transonic flows are obtained and the one that gives flows through a converging and diverging nozzle is considered in detail. This solution consists of four branches of which two are rejected because of singularities. Of the remaining two branches, one gives pure supersonic flow and the other gives taylor's type of flow with a local supersonic region in the throat. By varying a parameter, the latter branch approaches two asymptotes which yield meyer's type of asymmetrical flows."},
{"title":"Clamped short oval cylindrical shells under hydrostatic pressure.","url":"cran.html#doc765","description":"Vafakos, W.P. J. Ae.scs. 29, 1962, 1347. The principle of the minimum of the total potential is employed to obtain stresses and displacements for clamped, short, oval cylindrical shells under hydrostatic pressure. Classical shell theory, in which buckling effects are not considered, was used. A fourier series is assumed for the deflections in the closed circumferential direction so that the partial differential equations of equilibrium are replaced by a set of ordinary differential equations. The energy solution is compared with a simplified approximation which can be considered an equivalent circular cylinder solution. Graphs of the significant stresses and displacements are presented for oval cylinders having major to minor axis ratios of 1.10, 1.30, and 1.50. It is shown that the maximum stresses and displacements increase significantly as the major to minor axis ratio is increased."},
{"description":"Glauert, M.B. J. Ae. Scs. 1962, 540. Article is a continuation of an earlier note on papers by li on a semiinfinite plate in a uniform shear flow. Li had deduced from the form of his equations that stream vorticity caused an induced pressure gradient in the flow. Later papers by li and murray (amr 15(1962), rev. 7157) support the induced pressure gradient theory. The author notes, however, that the mathematics used by li and murray are not acceptable and the problem thus not resolved. The present note sets up simple models of complete flows examinable by elementary means. Author holds that analyses demonstrate conclusively that no pressure gradient is induced in the boundary layer on a flat plate in a limited region of shear flow. He notes that the original question in the case of unbounded shear remains obscure--and anyway an unlimited shear layer is not of great practical importance.","title":"The pressure gradient induced by shear flow past a flat plate.","url":"cran.html#doc388"},
{"url":"cran.html#doc287","title":"Some theoretical low-speed loading characteristics of swept wings in roll and sideslip.","description":"Bird, J.D. Naca r969, 1950. The weissinger method for determining additional span loading for incompressible flow is used to find the damping in roll, the lateral center of pressure of the rolling load, and the span loading coefficients caused by rolling for wing plan forms of various aspect ratios, taper ratios, and sweep angles. In addition, the applicability of the method to the determination of certain other aerodynamic derivatives is investigated, and corrections for the first-order effects of compressibility are indicated. The agreement obtained between experimentally and theoretically determined values for the aerodynamic coefficients indicates that the method of weissinger is well suited to the calculation of the additional span loading caused by rolling and for the calculation of such resulting aerodynamic derivatives of wings as do not involve considerations of tip suction."},
{"title":"Preliminary analysis of axial flow compressors having supersonic velocity at the entrance of the stator.","url":"cran.html#doc426","description":"Ferri, A. Naca rm l9g06, 1949. A supersonic compressor design having supersonic velocity at the entrance of the stator is analyzed on the assumption of two-dimensional flow. The rotor and stator losses assumed in the analysis are based on the results of preliminary supersonic cascade tests. The results of the analysis show that compression ratios per stage of 6 to 10 can be obtained with adiabatic efficiency between 70 and 80 percent. Consideration is also given in the analysis to the starting, stability, and range of efficient performance of this type of compressor. The desirability of employing variable-geometry stators and adjustable inlet guide vanes is indicated. Although either supersonic or subsonic axial component of velocity at the stator entrance can be used, the cascade test results suggest that higher pressure recovery can be obtained if the axial component is supersonic."},
{"description":"Craven, A.H. Coa R.144, 1960. The effects on base pressure of jet mach number, free stream reynolds number and jet to base diameter ratio have been investigated experimentally.